Citation
Fatigue analysis of Evans Avenue bridge over Santa Fe Drive

Material Information

Title:
Fatigue analysis of Evans Avenue bridge over Santa Fe Drive
Creator:
Cole, Elisabeth Jaclyn
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
1 electronic file. : ;

Subjects

Subjects / Keywords:
Bridges -- Maintenance and repair -- Colorado ( lcsh )
Bridges -- Maintenance and repair -- United States ( lcsh )
Iron and steel bridges -- Fatigue -- United States ( lcsh )
Bridges -- Maintenance and repair ( fast )
Iron and steel bridges -- Fatigue ( fast )
Colorado ( fast )
United States ( fast )
Genre:
non-fiction ( marcgt )

Notes

Review:
The West Evans Avenue Bridge over South Santa Fe Drive was built in 1972. In 2009, an inspection was completed to assess the current condition of the bridge for recommendations on an upcoming rehabilitation project. Initial results through use of visual inspection and analysis for compliance with the AASHTO Manual for Bridge Evaluation and the AASHTO LRFD Bridge Design Specifications determined retrofits to the steel girders containing the partial length cover plates would be necessary to extend the fatigue life of the bridge for another 20 plus years costing the City and County of Denver an additional one million dollars. Due to the age of the bridge the most conservative estimates were used in the calculations for determining the remaining fatigue life of the steel girders. This prompted field-testing to measure the actual stress ranges on the bridge. 20 strain gauges were placed on the bottom flanges of the steel girders of concern from March 8, 2011, through April 11, 2011. The remaining fatigue life of the bridge was calculated at 53 years requiring no retrofits to the existing steel girders at this time. This thesis presents the analysis of the AASHTO calculations requiring retrofits for the steel girders, the procedure and results of the strain gauge testing resulting in no retrofits, and a cost savings for the City and County of Denver by completing both fatigue analysis.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Civil engineering
Bibliography:
Includes bibliographic references.
General Note:
Department of Civil Engineering
Statement of Responsibility:
by Elisabeth Jaclyn Cole.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
861758507 ( OCLC )
ocn861758507

Downloads

This item has the following downloads:


Full Text
FATIGUE ANALYSIS OF EVANS AVENUE
BRIDGE OVER SANTA FE DRIVE
by
Elisabeth Jaclyn Cole
B.S., University of Colorado Boulder, 1996
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado Denver in partial fulfillment
of the requirements for the degree of
Masters of Science
Civil Engineering
2012


This thesis for the Masters of Science degree by
Elisabeth Jaclyn Cole
has been approved for the
Civil Engineering Program
Dr. Kevin L. Rens, Chair/Advisor
Dr. Yail Kim
Dr. Rui Liu
November 28, 2012


Cole, Elisabeth (M.S., Civil Engineering)
Fatigue Analysis of Evans Avenue Bridge Over Santa Fe Drive
Thesis directed by Professor Dr. Kevin L. Rens
ABSTRACT
The West Evans Avenue Bridge over South Santa Fe Drive was built in 1972.
In 2009, an inspection was completed to assess the current condition of the
bridge for recommendations on an upcoming rehabilitation project. Initial results
through use of visual inspection and analysis for compliance with the AASFITO
Manual for Bridge Evaluation and the AASFITO LRFD Bridge Design
Specifications determined retrofits to the steel girders containing the partial
length cover plates would be necessary to extend the fatigue life of the bridge for
another 20 plus years costing the City and County of Denver an additional one
million dollars.
Due to the age of the bridge the most conservative estimates were used in
the calculations for determining the remaining fatigue life of the steel girders.
This prompted field-testing to measure the actual stress ranges on the bridge.
20 strain gauges were placed on the bottom flanges of the steel girders of
concern from March 8, 2011, through April 11,2011. The remaining fatigue life
of the bridge was calculated at 53 years requiring no retrofits to the existing steel
girders at this time. This thesis presents the analysis of the AASFITO
calculations requiring retrofits for the steel girders, the procedure and results of


the strain gauge testing resulting in no retrofits, and a cost savings for the City
and County of Denver by completing both fatigue analysis.
The form and content of this abstract are approved. I recommend its
publication.
Approved: Kevin L. Rens
IV


TABLE OF CONTENTS
Tables.................................................................ix
Figures................................................................xi
Chapter
1. Introduction........................................................1
2. Literature Review of Fatigue........................................4
2.1 Brief Metal Fatigue History.........................................4
2.2 Fatigue Threshold and Crack Initiation.............................5
2.3 AASHTO Fatigue Design and Evaluation...............................6
2.4 Field Strain Measurements.........................................11
3. History of the Evans Bridge........................................13
3.1 Construction History...............................................13
3.2 Repair History....................................................15
3.3 Inspection History................................................18
3.3.1 Biannual Inspections.............................................18
3.3.2 Additional Inspections and Analysis..............................21
3.3.2.1 1996 Column Capacity Analysis..................................22
3.3.2.2 2000 Bearing Field Inspection..................................23
3.3.2.3 2001 Movement and Stress Study Report..........................26
3.3.2.4 2009 Condition Inspection......................................29
v


4. Rehabilitation Project...............................................30
4.1 Project Initiation...................................................30
4.2 Visual Inspection...................................................30
5. Visual Inspection and Fatigue Life Design............................32
5.1 Traffic Counts.......................................................32
5.2 Bridge Girder Modeling..............................................32
5.3 Fatigue Analysis....................................................33
5.3.1 Stress Range.......................................................33
5.3.2 Nominal Fatigue Resistance........................................34
5.3.2.1 Fatigue Live Load Factor.........................................34
5.3.2.2 Live Load Distribution Factor....................................35
5.3.2.2.1 Moment Distribution on Exterior Girders........................35
5.3.2.2.2 Moment Distribution on Interior Girders.......................37
5.3.3 Infinite Fatigue Life.............................................38
5.3.4 Finite Fatigue Life...............................................42
6. Strain Transducer Testing Procedures.................................46
6.1 Strain Transducer History..........................................46
6.2 Strain Transducer Development......................................46
6.3 Strain Transducer Installation.....................................47
6.4 Transducer Removal..................................................53
7. Strain Transducer Data Collection and Analysis.......................54
7.1 Traffic Counts......................................................54
VI


7.1.1 Traffic Data...................................................54
7.1.2 Average Daily Truck Traffic....................................55
7.2 Control Test...................................................55
7.2.1 Control Test...................................................55
7.2.2 Control Test Results...........................................58
7.3 Stress Cycles...................................................64
7.3.1 Stress Cycle Counts............................................64
7.3.2 Stress Cycle Data Analysis for 80 Girder Span.................67
7.3.3 Stress Cycle Data Analysis for 95 Girder Span.................76
8. Results...........................................................79
8.1 Visual Inspection Fatigue Life Design Results....................79
8.2 Strain Transducer Fatigue Life Results..........................80
9. Cost Comparison...................................................83
10. Conclusions and Future Research..................................84
10.1 Conclusions.....................................................84
10.2 Future Research.................................................85
References...........................................................88
Appendix
A. Section Properties of 80 Span....................................92
B. Section Properties of 95Span.....................................94
C. 80 Span Visual Inspection Calculations...........................96
D. 95 Span Visual Inspection Calculations..........................100
vii


E. ADTT Counts
104
F. 80 Span Strain Gauge Analysis..........................................109
G. 95 Span Adjusted Calculations..........................................119
viii


LIST OF TABLES
Table
5.1 80 Span Girder Stress Distribution...........................41
5.2 80 Span Girder Bottom Flange Fatigue Life Check..............42
5.3 80 Span Girder Bottom Flange Fatigue Life....................45
5.4 95 Span Girder Bottom Flange Fatigue Life....................45
7.1 Control Test Results Summary..................................63
7.2 Stress Cycle Count Summary....................................65
7.3 Estimated Minimum Finite Life of 80 Span Girders with
Minimum Stress Range of 1.0 to 1.5 ksi.......................71
7.4 Estimated Minimum Finite Life of 80 Span Girders with
Minimum Stress Range of 2.0 to 2.5 ksi.......................73
7.5 Estimated Evaluation Finite Life of 80 Span Girders with
Minimum Stress Range of 2.0 to 2.5 ksi.......................75
7.6 Estimated Mean Finite Life of 80 Span Girders with
Minimum Stress Range of 2.0 to 2.5 ksi.......................75
7.7 Calculated Fatigue Life for the 95 Span Girders..............78
IX


8.1 Estimated Remaining Design Fatigue Life for 80 Span..........80
8.2 Estimated Remaining Design Fatigue Life for 95 Span..........80
8.3 Estimated Remaining Evaluation Fatigue Life for 80 Span......81
8.4 Estimated Remaining Evaluation Fatigue Life for 95 Span......82
x


LIST OF FIGURES
Figure
2.1 S-N Curve for AASHTO Detail Categories............................8
3.1 Evans Bridge Plan and Elevation 1966.............................14
3.2 Rusted Steel Girder Below Santa Fe Ramp Abutment.................17
3.3 Flashing Below Abutment and New Paint on Steel Girder............18
3.4 Evans Bridge Elevation 1996......................................22
3.5 Pier 6 Expansion Bearing.........................................25
3.6 Deteriorated Concrete Pier Cap...................................28
5.1 Evans Bridge 2009 ADTT Counts....................................32
5.2 Evans Bridge Cross Section.......................................37
6.1 BDI ST350 Strain Transducer......................................47
6.2 Strain Transducer Locations......................................48
6.3 Transducer Location to Partial Cover Plate......................49
6.4 Aluminum Cover Around Transducer.................................50
6.5 14 of 20 Installed Transducers...................................51
6.6 Structural Monitoring System.....................................52
6.7 Structural Monitoring System Power Source........................52
7.1 Truck at Base of Evans Bridge for Control Test...................56
7.2 Truck Climbing Ramp of Evans Bridge for Control Test.............56
XI


7.3 Truck Approaching Strain Transducers
During Control Test.........................................57
7.4 Truck Completing Control Test................................57
7.5 Control Test 1 Results for Transducers F1-K1.................59
7.6 Control Test 2 Results for Transducers F1-K1.................60
7.7 Control Test 3 Results for Transducers F1-K1.................61
7.8 Control Test 4 Results for Transducers F1-K1.................62
7.9 Strain Transducer Locations..................................67
xii


1. Introduction
Fatigue failure was a phenomenon that started gaining attention in the mid
19th century and by the beginning of the 20th century researchers had uncovered
the causes of fatigue. The researchers began identifying fatigue thresholds for
various materials, although fatigue thresholds were not easily quantifiable
because of the scatter in the data. This was not due to lack of research as it was
determined that fatigue is largely based on impurities of the member and each
member can contain different amounts of impurities increasing or decreasing the
fatigue lives of members fabricated from the same materials.
Throughout the 20th century, researchers and engineers continued evaluating
the causes and effects of fatigue in steel members of different sizes and shapes
and began creating bridge design requirements. Although much progress was
made within a short amount of time, bridge failures were increasing in the mid
20th century. In 1978, due to the increase in bridge failures, the Federal Flighway
Administration began mandating that all bridges longer than 20 would require
biannual inspections (Federal Highway Administration, n.d.). The biannual
inspections aided in the engineers awareness of the bridge condition; however,
evaluating a bridge for fatigue failure was still nonexistent. Utilizing fatigue
design for the assessment of an existing bridge was proving to be overly
conservative resulting in requiring expensive repairs to the structures.
Methods for evaluating existing bridges for fatigue began to emerge in the
late 1980s. By 1990, an evaluation guide of existing steel bridges was created
1


providing an assessment of existing bridges. This was followed by development
of better evaluation techniques by the turn of the 21st century. Current evaluation
methods provide the most accurate results of bridge fatigue analysis for
measurements taken in the field, including actual traffic data and strain
measurements gathered at fatigue critical details. Closer evaluation of these
methods will be looked at in a current project located in Denver, Colorado.
The West Evans Avenue Bridge, spanning over Santa Fe Drive, was built in
1972 and has been part of the City and County of Denvers biannual inspections
since the 1980s. During the life of the bridge both small and large-scale repairs
have been undertaken in an effort to maintain the bridges ability to publicly
operate. In 2009 the Evans Bridge was thoroughly inspected for an upcoming
rehabilitation project. The City and County of Denver was designing the
rehabilitation to last for the next 20 years and since fatigue in existing bridges
has been a problem, especially for older bridges, a fatigue analysis was
conducted on the steel girders of the Evans Bridge. The analysis was based on
visual inspection which required mostly fatigue design values to be used, thus
creating a conservative estimate that the fatigue life of the bridge would not meet
the 20 year requirement.
Repairs and retrofits to the existing steel girders would make the girders
surpass the 20-year minimum, but would be very costly. Advances in the
collection of strain measurements provided opportunity for the bridge to be tested
for a minimal cost. Data was collected at the fatigue prone locations and the
fatigue life was reanalyzed. This thesis analyzes the fatigue life of the steel
2


girders using both the visual inspection method and the data collected in the
field. This includes comparing the results and costs associated with each
methods solution.
3


2. Literature Review
2.1 Brief Metal Fatigue History
Documented research on metal fatigue began in the 1830s following multiple
unexpected mechanical failures occurring after extended use (Frost et al., 1974).
These failures were caused in devices where low stresses were applied multiple
times. August Wohler, an early researcher of metal fatigue (Schijve, 2009), was
quoted with referring to fatigue as rupture of material may be caused by
repeated vibrations, none of which attain the absolute breaking limit
(Spangenburg, 1876). The idea Wohler presented was that materials under
repeated loadings could fail even if that load is below the fracture limit.
Wohler also determined that there is a stress range in which a material did
not fracture no matter the number of times the element was loaded (Frost et al.,
1974). This has become to be known as the fatigue limit or threshold, in which
each member has a stress limit where cyclic loads applied below the threshold
will give infinite life, and cyclic loads applied above the threshold but below the
fracture limit will provide a finite life span. Finite fatigue life is calculated by the
number of loadings a member can withstand before complete failure (Schijve,
2009; Pook, 2007).
Wohler was not the only researcher to come to this conclusion in the 19th
century. William Rankine discovered during the 19th century that the metal under
this repeated loading had a brittle appearance (Frost et al., 1974). This
discovery led to the idea that the metal would slowly deteriorate, becoming
4


crystalline and brittle in nature, which would ultimately produce a complete
failure. In the early 20th century Ewing and Humphrey further researched the
changing of the metallic properties on the surface of the element during the
process of the repeated loadings (Pook, 1983; Pook, 2007). Researchers have
also determined that developments in the metals during the fatigue tests can be
categorized into three phases; the crack initiation phase, crack growth phase,
and failure of the member (Zhou and Haidar, 2006; Schijve, 2009).
2.2 Fatigue Threshold and Crack Initiation
The crack initiation phase creates micro fractures in the surface of the
element in as little as one load cycle, provided the applied load is above the
fatigue threshold (Schijve, 2009). Micro fractures develop in the surface due to
stress concentrations at surface irregularities (Frost et al., 1974). Surface
irregularities can be attributed to various life stages including manufacturing,
surface preparation, and even environmental factors such as corrosion. This
variety of surface irregularities that each member has creates different lengths of
fatigue life, making it difficult to quantify exactly the length of fatigue life for each
type of material (Frost et al., 1974; Schijve, 2009). Not all micro fractures
develop into visible cracks, those that do take a long time to turn into visible
cracks, making the majority of the fatigue life in the crack initiation phase
(Schijve, 2009). This principle can redefine the fatigue threshold to the largest
stress amplitude which does not lead to continuous crack growth until failure
(Schijve, 2009, pg. 31).
5


Numerous experiments have been conducted to determine if increasing the
members size would increase the fatigue threshold. Bending fatigue tests have
proven that increasing the members size actually decreases the fatigue
threshold (Frost et al., 1974; Schijve, 2009). As previously stated the micro
fractures occur at surface imperfections containing a higher stress concentration.
With an increased member size, the probability of having such weak spots is
larger for a larger material surface area carrying the maximum stress cycle
(Schijve, 2009, pg. 153).
Welded locations have a higher probability of crack propagation at the toe of
the weld, largely due to two occurrences. Firstly, the weld can contain a large
number of defects. Secondly, because of the welding process, the contraction of
the weld when it cools creates residual stress within the weld (Poutiainen and
Marquis, 2005; Schijve, 2009; Pook, 2007). Fillet welds contain even higher
concentrations of stress than other types of welds, because the welds do not
penetrate through the entire member (Frost et al., 1974). Peening welds is a
method of reducing the number of imperfections with in the weld, as well as
loading the weld with residual compression. Current research on peened
highway bridge welds has proven to benefit the fatigue life of a large range of
probable bridge loading conditions (Ghahremani and Walbridge, 2010).
2.3 AASHTO Fatigue Design and Evaluation
As bridge failures became an increasing issue in the United States,
culminating with the 1967 collapse of the Silver Bridge due to fatigue failure of an
6


eyebar supporting the main span (Connor et al., 2005), the Federal Highway
Administration began implementing policies for bridge inspections. The
American Association of State Highway and Transportation Officials (AASHTO)
published their 10th Edition of the AASHTO Standard Specifications for Highway
Bridges in 1969. This edition was the second appearance of fatigue design
provisions, the first published in 1965. However, the 10th Edition determined an
allowable fatigue stress from such factors as the applied load, highway
classification, steel strength, detail type, and ratio of minimum to maximum stress
(Bowman et al., 2012).
The 12th Edition of the AASHTO Standard Specifications for Highway Bridges,
published in 1977, addressed common details in steel bridges that were
considered fatigue sensitive (Bowman et al., 2012). This list of details, currently
known as the detail categories, ranged from A through F, although some
changes have occurred and the list no longer includes F, the detail categories for
the most part are the same (Frost et al., 1974; Bowman et al., 2012). In addition
to the detail categories, the 12th Edition also included a stress range. As
identified by studies and research, the stress range was determined to be a
function of the detail category and number of applied cycles, not the strength of
the material (Bowman et al., 2012).
AASHTO employed the S-N curve method for determining fatigue life, which
uses the stress range and number of cycles applied. To determine a fatigue
threshold, as well as the number of cycles at different stresses the detail was
able to withstand, each detail category was thoroughly tested by National
7


from the mean), and the minimum fatigue life as 2% probability of failure (two
standard deviations from the mean) (Bowman et al., 2012; AASHTO, 2011).
As reconstruction and retrofits to bridges can be costly, the resistance factor
provides a valuable tool for the evaluation process. Provided no cracks are
visible at the fracture critical detail, AASHTO requires retrofits to all cracked
members, the resistance factor used is determined by the engineers judgment.
Although it is possible to achieve negative remaining fatigue life, which means
that the detail has surpassed the resistance factors probability of failure
(Bowman et al., 2012), it is quite common for a bridge to achieve a greater
fatigue life than that provided by minimum design, or 2% probability of failure. A
steel detail can still surpass the mean resistance factor, as it is a 50% probability
of failure, meaning 50% of the tests conducted have surpassed that value. This
is why when evaluating an existing bridge it is up to the engineer to decide which
resistance factor is used in determining remaining fatigue life.
Following the improvements to the LRFR Manual, AASHTO published the
Manual for Bridge Evaluation (MBE) in 2008 and issued a 2nd Edition in 2011.
The MBE addressed the use of collected field strain data, used in lieu of the
calculated stress range, which is more accurate, requires less factors of safety,
and ultimately produces longer fatigue life with more accuracy than the design
method (Bowman et al., 2012; AASHTO, 2011).
10


2.4 Field Strain Measurements
Field strain measurements have been increasing in popularity in order to
avoid costly retrofits to existing bridges (Zhou, 2006). Developments in the strain
gauge monitoring systems have created portable systems that can collect live
data using web-based applications (Howell and Shenton, 2006). One
consideration for field measurements is the inclusion of all the stress cycles
collected, even those below fatigue threshold. For lower fatigue categories, D, E,
and E, the percentage of cycles below the fatigue threshold account for the
majority of the vehicle traffic (Zhou, 2006). Including all of the gathered stress
cycles lowers the calculated stress range, ultimately providing an overestimation
of fatigue life. Some probabilistic methods have been evaluated to determine the
cut-off of the stress range (Kwon and Frangopol, 2010), while other cut-off
methods include using all stresses above 50% of the constant amplitude fatigue
limit (Zhou, 2006), and still others truncate the stress range at the constant
amplitude fatigue threshold (Alampalli and Lund, 2006). The ultimate decision
relies upon engineering judgment as to where to remove the lower stress cycles
in an effort to produce an acceptable stress range.
Using a strain gauge monitoring system, the New York State Patroon Island
Bridge was evaluated to have a minimum safe fatigue life of 27 years at a detail
category E location (Alampalli and Lund, 2006). The Cleveland Central Viaduct
was found to have insufficient remaining fatigue life using the AASHTO visual
inspection evaluation method, but field testing proved the bridge to have infinite
fatigue based on the most fatigue prone detail location (Zhou, 2006). As
11


concluded by Kwon and Frangopol, The field monitoring data can be
successfully used for fatigue reliability assessment and fatigue life prediction of
existing steel bridges (2010, pg. 1232).
12


3. History of the Evans Bridge
3.1 Construction History
Drawings for the Evans Bridge over Santa Fe Drive in Denver, Colorado, date
back to 1966; there is no recorded documentation prior to this. Only one page of
the 1966 drawings was archived, which consists of plan and elevation views of
the bridge and a note stating that these drawings are for reference only and not
part of the construction plans. Although this drawing was not part of the
construction set, it has the girder sizes and spans that were used in the final
construction of the bridge, as shown in Figure 3.1.
13


Figure 3.1 Evans Bridge Plan and Elevation 1966
(City and County of Denver West Evans Avenue and South
Santa Fe Drive Grade Separation Plan & Profile, Project
Number 9204, 1966)
The City and County of Denver Public Works Division (CCD) submitted
final drawings for approval and construction in August 1971. These
drawings included the structure, retaining walls, abutments, deck, bearing
and expansion devices, approach details, railway signals, railroad grading,
painting, lighting, and guardrail layouts. Construction of the bridge began
in 1972 and was completed later that year. The bridge was constructed
with a composite concrete deck, and consists of 12 hot rolled steel I-
beams over 9 spans with an overall length of 765 feet.
14


In 1983, the Colorado Department of Transportation (CDOT) made
plans to construct ramps connecting Santa Fe Drive with Evans Avenue.
However, in order for this construction to progress, CDOT needed to gain
approval from CCD to connect these ramps to the existing Evans Bridge.
CCD agreed to this construction and designed modifications to the bridge
to allow ramp access. This required removal of the barrier walls and
construction of new turn lanes and traffic signals. CDOT and CCD worked
together to design the ramps to fit the current bridge. However, the bridge
and the ramps remain two separate entities; CCD maintains the bridge,
while CDOT maintains the ramps.
3.2 Repair History
Although a few repairs were made in 1983 with the addition of CDOTs
ramps, there were many more to be done to keep the bridge in good
working order. 1985 brought on the first major round of repairs to the
bridge. The repairs included completely resurfacing the road, replacing the
sidewalks, railings, and concrete barriers, placing new backfill around the
structure, and updating the landscape.
The next round of bridge repairs came in 1995, following a field
inspection in 1994. Refer to section 3.3 for more information regarding the
1994 inspection. Repairs made to the Evans Bridge at this time were the
15


expansion joints, the fixed and expansion bearings, abutments, and new
asphalt resurfacing. These repairs continued through 1997.
In 2010, the steel girders below the abutments of the Santa Fe Drive
ramps were severely rusted and required attention, refer to Figure 3.2.
The high levels of rust were due to a deteriorating abutment condition
causing water to leak through. Although CDOT owns and operates the
ramps connecting Santa Fe Drive and Evans Avenue, they did not want
pay for half of a new abutment joint at these locations. This required that
CCD install flashing to avoid water damage to the steel girders below,
since they were unable to install a new abutment. With flashing installed
to divert leaks from affecting the steel girders, the girders were then
grinded down to remove the rust and then repainted, refer to Figure 3.3.
16


17


Figure 3.3 Flashing Below Abutment and New Paint on Steel Girder
3.3 Inspection History
3.3.1 Biannual Inspections
In 1980, the Federal Highway Administration implemented a policy that
requires all bridges with spans twenty feet or longer to be inspected on a
biannual basis. Due to this Federal policy, CCD started a bridge
inspection program for the 538 bridges within the limits of CCD's
jurisdiction. All of CCDs bridges are inspected either biannually or tri-
annually based on the bridges length. Bridges with twenty foot spans or
18


longer are inspected every other year, which account for 207 of CCDs
bridges. The 331 CCD bridges with spans less than twenty feet are
inspected every third year. Inspections of smaller bridges are not required
by the Federal Highway Administration, but have been completed by CCD
to maintain records of all the bridges in Denver.
Records of the Evans Bridge inspections are available at the City and
County of Denver Public Works Division office for every two years starting
in 1994. Inspection reports prior to 1994 have been archived and have
proved difficult to retrieve. The 1994 inspection reported poor asphalt
conditions, moderate damage to the expansion joints, light rusting through
the steel girder paint, poor bearings, severe spalling of the concrete caps,
and moderate delamination of the concrete columns. The condition of
expansion joints were poor and needed urgent repairs (LONCO, 1994).
This inspection report prompted the repairs made in 1995.
Asphalt conditions of the 1994 inspection had worsened by the 1996
inspection, extending a continuation of repairs into 1997. Required repairs
from this inspection were the expansion joints at the abutments due to
leaking. Other concerns were the cracking concrete at the railing
connections, cracking on the bottom of the concrete deck, joint separation
of the wingwall, and deterioration of the concrete curbs and sidewalks
(LONCO, 1996).
19


Following the repairs in 1997, a final inspection was completed and
resulted in no urgent repairs. Maintaining the two-year inspection cycle,
1998 also warranted no urgent repairs. The majority of the comments in
the 1998 inspection report stated that the repair had been made in 1997,
however, there were still a few programmed repairs and general
maintenance items, such as cleaning deck drains, patching potholes, and
removing sand and gravel from the sidewalks (LONCO, 1998).
Inspections completed in 2000, 2002, 2004, and 2006, resulted in no
urgent repairs. However, programmed repairs and safety improvements
increased exponentially over the four inspections (LONCO, 2000; LONCO,
2002; LONCO, 2004; LONCO, 2006). The 2000 inspection report listed
cleaning deck drains, patching potholes, and installing safety markers as
the improvements and future repairs, amounting to $1,400. This is in
contrast to the 2006 report which listed patching potholes at multiple
locations, cleaning drains, replacing rubber fillers at ramp connections,
painting girders, rehabilitating delaminated concrete cap, installing safety
reflectors, replace missing posts, and installing a cover over the J-box.
The 2006 programmed repairs and safety improvements would cost
$32,300 to complete.
The inspection completed in 2008 used a new reporting system
employed by CCD. Each item needing attention had a priority designation
20


assigned. No urgent repairs were listed in this report. Installing safety
markers and replacing missing rails were noted as safety concerns.
Replacing expansion joints, and cleaning and painting the bearings were
listed as programmed repairs. Maintenance issues were cleaning the
deck drains, patching potholes and spalls, and painting the railing. The
estimated cost of these repairs came to $31,800, which was in alignment
to the approximate costs estimated in 2006, including the future repair
cost (Short Elliott Hendrickson Inc., 2008).
The 2010, the biannual inspection report read similarly to the 2008
inspection; however, a major difference in the 2010 inspection report was
an increase in quantity of the repairs with an estimated cost of $40,560.
The additional cost of approximately $8,000 implies that the bridge had
further degraded since 2008, which is evident by a 60% increase in the
number of potholes (Short Elliott Hendrickson Inc., 2010).
3.3.2 Additional Inspections and Analysis
In addition to the biannual inspections, CCD has historically contracted
with private companies to complete additional inspections on the Evans
Bridge. The additional inspections are requested by CCD for reasons
deemed necessary for the assurance of the bridge safety. Typically, the
21


additional inspections are completed due to questionable quality of major
structural elements that could require large scale, expensive repairs.
3.3.2.1 1996 Column Capacity Analysis
The first additional inspection in this series was completed in 1996, by
URS Consultants Inc., for the capacity analysis of a deteriorated column
located to the south side of bent #6, refer to Figure 3.4 below. The bents
sit atop a Teflon bearing material which ideally creates a frictionless
connection to prevent the transfer of shear and moment to the concrete
columns. Spalling concrete, rusted bearing pads, and missing Teflon on
top of the bearing pad caused concern that the connection was no longer
frictionless and causing the break down of the column, prompting an in
depth analysis of the column.
Figure 3.4 Evans Bridge Elevation 1996
(City and County of Denver West Evans Avenue Viaduct
Resurfacing and Expansion Joint Replacement Project,
Project Number 95-294A, 1996)
22


The west side of Bent #6 is at an existing expansion joint. Thermal
expansion of the bridge will engage the bent forcing it to move. Ideally,
Bent #6 will slide frictionless atop a bearing which will not transfer shear or
moment into the concrete column under the bearing. URS analyzed this
ideal condition and confirmed that no shear or moment would be
transferred into the column below (Hawkins, 1996).
Based on information provided from CCD, about the current condition
of the spalling column and rusted bearing pad, URS completed a second
analysis of the column under the poor conditions. URS assumed the
connection was fixed, and reported that the analysis showed both moment
and shear transferred from the bent into the column. However, the
amount of shear and moment transferred was still within the acceptable
factor of safety limits. URS also reported that assuming a fixed condition
was conservative, since it was unlikely that the bent would not slide given
enough force. The final determination to the cause of the spalling
concrete column and rusted bearing was from the leaking expansion joint
above the west side of Bent #6.
3.3.2.2 2000 Bearing Field Inspection
During CCDs programmed 2000 inspection, observations that the
expansion bearings on Pier 6 and the east abutment were not sliding
23


caused concern. Further apprehension was caused by the rust pack and
deformation present between the stainless steel plates, sole plates, and
Teflon pads of the expansion bearings. These concerns required CCD to
hire a consultant to complete a more detailed inspection.
URS Greiner Woodward Clyde (URS), the same company who
analyzed the column capacity in 1996, was consulted again to conduct a
bearing field inspection. This inspection was to complete a movement
study of Pier 6 while also determining the column profile and conducting a
bearing inspection for both Pier 6 and the east abutment (Li, 2000). The
objectives of the inspection were to record the bearing condition, measure
the bearings physical dimensions, observe the expansion bearings
performance, and make rehabilitation recommendations.
URS confirmed CCDs inspection results that the expansion bearings
at Pier 6 and the east abutment were no longer sliding. The determined
causes of this were due to the rust pack around the bearing area, as well
as deformation of the plates and Teflon preventing the bearing from
sliding, as shown in Figure 3.5. The expansion joint above Pier 6
appeared to be leaking which was a probable cause for the rust pack of
the expansion bearing. Replacement of both bearings was recommended
since they were no longer functioning as required per the original design.
24


Figure 3.5 Pier 6 Expansion Bearing (Li, 2000)
Although not within the scope of work, URS noted other problem areas
they observed in their report. None of the other expansion bearings were
sliding and performing as intended, requiring replacement of the
expansion bearings. Some of the girder ends were observed to have rust;
however, no section loss was found, therefore removing the rust and
repainting would be a sufficient repair. Areas of concrete on the deck
overhang were delaminating, so removing the delaminated piece and
patching the area was recommended for the safety of the vehicles
travelling on Santa Fe Drive. Rust was visible on the bottom of pier caps
for Pier 3 and 6, suggesting deteriorating reinforcement, exposing the
25


reinforcement would be required to determine the extent of the corrosion.
A vertical crack in the Pier 6 concrete cap cantilever was also observed
and URS recommended running a section analysis to determine the cause
and repair of the cap. Lastly, the space between the girder and the west
abutment was a concern, requiring an expansion analysis on the thermal
movement to determine adequate spacing.
3.3.2.3 2001 Movement and Stress Study Report
Based on URSs recommendations, CCD contracted with them to
complete a movement and stress study. Between March 2000 and March
2001, URS performed four measurements to determine the movement of
Pier 6. Other organizations were contracted to aid in the measurements
which included Atkinson-Noland & Associates for the condition of the
cracked pier cap at Pier 6, and the University of Colorado Denver, lead by
Dr. Kevin Rens, for the condition of the corroded steel girders.
URS utilized a standard surveying approach to collect data for the
movement of Pier 6 (Li, 2001). Tapes mounted to the pier cap and
column were read from set points. From the readings during the four
visits, the top of the column was found to be deflecting in the east-west
direction creating a moment of 50% of the columns flexural capacity. It
was recommended to check the column when new expansion bearings
26


are installed. The deflection in the north-south direction was found to be
negligible.
Atkinson-Noland & Associates conducted measurements on the crack
in the cantilever cap of Pier 6 using tomography to determine the size and
location of the cracks (Rens & Transue, 2002). The vertical crack was
discovered to be approximately 8 inches deep at the top of the cap and
completely through at the lower portion of the cap, refer to Figure 3.6.
URS took this data and analyzed the tension. The pier cap was
determined to have sufficient capacity remaining; however, it was
recommended to seal or patch the crack to prevent further damage.
27


Figure 3.6 Deteriorated Concrete Pier Cap
Dr. Kevin Rens and his research assistants from the University of
Colorado Denver took measurements on the corroded steel girders using
an ultrasonic testing method to determine the amount of steel lost. The
measurements gathered revealed that 21 % of the steel web was lost at
the worst location (Li, 2001). Even though there was a loss in the section,
the web thickness remaining was still adequate based on the HS20 live
load requirements. Having an adequate section repairing the girders
would consist of cleaning off the rust and repainting the steel.
28


3.3.2.4 2009 Condition Inspection
As the condition of the Evans Bridge worsened between 2000 and
2008, CCD contracted Felsburg Holt & Ullevig (FHU) to complete a
condition Inspection report in 2009. FHU was to also provide
recommendations to rehabilitate the bridge to a 30% level. The findings
and recommendations are discussed in chapter 4.
29


4. Rehabilitation Project
4.1 Project Initiation
CCDs biannual inspections from 2000 through 2008 showed that the Evans
Bridge was deteriorating and needed at least $31,800 in repairs. The 2008
inspection prompted repairs to the steel girders below the abutments of the
adjoining ramps to Santa Fe Drive because of the severity of the corrosion. Due
to the deteriorating condition of the bridge, CCD contracted with FHU in 2009 to
complete a thorough condition inspection. The purpose of this inspection was to
determine the actual condition of both structural and non-structural components,
and to make repair recommendations for a rehabilitation project.
4.2 Visual Inspection
FFIU contracted with LONCO to aid in the inspection. The inspection began
on June 8, 2009, and took most of two weeks to complete, although some
portions of the inspection were not completed until September 2009 (Felsburg et
al, 2009). All elements were inspected for code compliance as well as the
general condition.
Recommendations for the repairs to the above the deck portion of the bridge
was to replace the asphalt overlay, concrete median, and concrete barrier walls
due to poor or deteriorating conditions. Replacement of the drainage system
was recommended as it was found to be clogged and no longer functioning. The
30


railings on the concrete barrier walls did not show significant damage, but
replacement was recommended since they did not meet current code standards.
The inspection of the concrete deck was based on findings from the
underside of the deck, since the topside is currently covered with asphalt. Areas
under deck displayed cracking, spalling, and efflorescence. Most of the
deteriorated areas were under the expansion joints on the north and south edges
of the bridge. Repairing the damaged areas was recommended.
A previous inspection by URS in 2000 recommended replacing all of the
expansion bearings as they were not functioning as intended due to corrosion
and deterioration. As the bearings had not yet been replaced, and are still not
functioning, FHU recommended that all expansion bearings be replaced.
The final area inspected was the steel girders, as the girders were in a
corroding condition near the ramp abutments discovered in the 2008 inspection.
Outside of the rust locations, the girders appeared to be in good condition. FHU
took note of the fatigue critical locations at the ends of the partial length cover
plates. Due to the age of the bridge, FHU and CCD decided to investigate the
condition of the fatigue sensitive details to determine the remaining fatigue life of
the girders in order to insure an additional 20 years of life to the bridge.
31


5. Visual Inspection and Fatigue Life Design
5.1 Traffic Counts
LONCO, with the help of CCD, collected traffic counts on the Evans Bridge in
May 2009. From the collected data, LONCO determined the worst-case scenario
of truck traffic across both the 80 and 95 bridge spans. The worst-case for the
80 span was 1,510 trucks which occurred in the east bound direction, on the
west side of the bridge (over spans 1,2, and 3) prior to the traffic entering onto
Santa Fe Drive (Figure 5.1) which accounted for 11 % of the total traffic. For the
95 span, the worst-case scenario was in the west-bound direction at 1,189
trucks, which accounted for 7.8% of the total traffic.
Figure 5.1 Evans Bridge 2009 ADTT Counts
(Adapted from Felsburg et al, 2009)
5.2 Bridge Girder Modeling
The girder system of the bridge has partial-length cover plates on various
portions of each girder. There are a variety of cover plate configurations
including; sections of girders which have cover plates on the top and bottom
32


flanges, sections that have cover plates on the bottom flange only, and sections
which create a composite section with the concrete deck above. Due to the
complexities of these sections and a moving live load, more accurate results will
be produced by modeling both the 80 and 95 3-span girders in a structural
modeling software.
The software being used to evaluate the beam for the maximum positive and
negative moment stresses is STAAD. As specified in the LRFD an HS-20 design
truck load is used for fatigue analysis. The HS-20 design truck has a front axel
load of 8 kips spaced 14 from the second axel and the two rear axels are spaced
at 30 with 32 kips on each axel (AASHTO, 2012, pg. 3-28). The HS-20 design
truck load is placed on the girders in the STAAD model. No load factors are
applied to the model, as only the maximum positive and negative moments of
each detail location are desired in the output. Table 5.1 in Section 5.3.3 below
shows the maximum positive and negative moments calculated on the beam at
the specified locations from the modeling software.
5.3 Fatigue Analysis
5.3.1 Stress Range
As discussed in 2.1, fatigue failure is due to repeated cycles of stress
occurring above the fatigue threshold, which is significantly less than the amount
of stress required to cause yielding. Because of this, fatigue occurs within the
elastic range. The stress, o, at the girder details is a function of the bending
moment, M, over the elastic section modulus, S (Equation 5.1).
33


M
a =
s
5.1
Section moduli for the top and bottom of steel for each different detail were
calculated, as shown in Appendix A and B for calculations. Due to the
continuous 3-span condition of the girders, the STAAD model provided the
positive and negative bending moments. The negative and positive stresses for
the top and bottom flanges of the girder were calculated using Equation 5.1. The
live load stress range, due to the passage of fatigue load, Af, was then
determined for each flange from the calculated positive and negative stresses
(refer to Table 5.1 in section 5.3.3).
5.3.2 Nominal Fatigue Resistance
Two reductions are applied to the stress range to determine the nominal
fatigue resistance, (AF)n, the fatigue live load factor, yLL, and the live load
distribution factor for one traffic lane, g, Equation 5.2 (AASHTO, 2012).
(AF)n = #yLL(A/) 5.2
5.3.2.1 Fatigue Live Load Factor
The Fatigue category II is defined as Fatigue and fracture load combination
related to finite load-induced fatigue life (AASFITO, 2012, pg. 3-11). The
purpose of this analysis is to determine the load-induced finite fatigue life, making
34


Fatigue II the relevant category, as Fatigue I is used for infinite load-induced
fatigue (AASFITO, 2012, pg. 3-10). As demonstrated by the live load factor
table, Vll-0.75 for Fatigue II (AASFITO, 2012, pg. 3-13).
5.3.2.2 Live Load Distribution Factor
Moment and shear live load distribution need to be computed for both interior
and exterior beams. Each of the four distributions should be checked for one
design lane loaded and two or more design lanes loaded. This is not always true
as a clause states that for fatigue design the live load distribution factor should
be calculated for only one design lane loaded and that the multiple presence
factor of 1.2 included in the provided equations is to be removed (AASFITO,
2012, 3-18). As discussed in section 5.3.1, the stresses being calculated are
coming from the positive and negative moments at the specified locations
provided by the structural modeling software, meaning that only the moment
distribution load factor need be checked. Instead of eight calculations to
determine the governing live load distribution factor, g, only two need be
considered which is moment distribution for one design lane for an interior and
for an exterior girder.
5.3.2.2.1 Moment Distribution on Exterior Girders
Moment distribution on exterior girders due to one design lane loaded is
calculated using the lever rule. The lever rule assumes the deck is simply
supported between the exterior beam and the adjacent interior beam, and a
hinge at the interior beam so no additional forces transfer. Live load from the
35


design truck is applied 2 from the curb at the first truck wheel and the wheels are
spaced at 6 with an axial force applied at both tires. Summing the moments
around the interior beam provides the reaction at the exterior beam. Ignoring the
actual axial load and solving for the reaction at the exterior beam in terms of
variable P, provides a ratio of P; this ratio is the distribution factor applied to the
exterior girder.
In the case of the Evans Bridge the exterior girder is located 1-5 from the
outside face of the bridge, the girders are spaced at 6-10 on center, and the
outside face of the bridge to the end of the sidewalk measures 7-8 (refer to
Figure 5.2 below). The question here becomes, if there is no truck load on the
span between the exterior and adjacent interior girder, does the distribution factor
matter at the exterior girder? A distribution load can be solved for using the
pedestrian load, however, the pedestrian load will be minimal compared to a
truck load. By this rationale, the interior girders will have more load than the
exterior girder, and since the bridge is being evaluated on a design truck and not
pedestrian traffic, the calculated distribution factor should be based on the
moment distribution of one design lane loaded for an interior girder.
36


Figure 5.2 Evans Bridge Cross Section
(Felsburg et al, 2009)
5.3.2.2.2 Moment Distribution on Interior Girders
The live load distribution factor for interior girders, g, is a function of the
longitudinal stiffness parameter, Kg, girder spacing, S, girder length, L, and slab
thickness, ts (AASHTO, 2012 pg. 4-32). Where the stiffness parameter is a
function of the girder section properties, distance between centers of gravity, the
modular ratio of the girder and concrete deck, and Equation 5.3 through 5.5. The
stiffness parameter determines how stiff the girder is relative to the deck.
Kg = n(7 + Ael)
5.3
Where:
A = Cross-Sectional Area of the Girder
/ = Moment of Inertia of the Girder
eg = Distance between the Deck and Girder Centers of Gravity
37


n = Modular Ratio of Girder and Deck
5.4
Substituting Equation 5.4 into 5.3 gives:
5.5
Once the longitudinal stiffness parameter has been determined, the
distribution factor can be calculated using the equation for one design lane
loaded for a deck and beam bridge configuration (Equation 5.6).
The multiple presence factor mentioned in section 5.3.2.2 needs to be
removed from the distribution factor. Dividing the distribution factor by the 1.2
multiple presence factor gives a final distribution factor of 0.34 for the 80 span
and 0.33 for the 95 span.
5.3.3 Infinite Fatigue Life
Infinite fatigue life occurs when the maximum stress, (Af)max, is less than the
fatigue threshold, (AF)Th, of the specific detail category. The maximum stress is
5.6
38


a function of the effective stress, (Af)eff, which is a function of the nominal stress,
(AF)n, calculated in section 5.3.2 (refer to Equation 5.7 through 5.9). In this
check AASHTO assumes that no load applied will be greater than two times the
calculated effective stress, providing a factor of safety for determining whether a
detail has infinite life.
(A f)max = 2(A Heff 5.7
(Af)eff = RsiA^n 5.8
Where:
Rs = Partial Load Factor (AASHTO, 2011, pg. 7-3)
When designing versus evaluating a bridge from collected data, the partial
load factor is 1.0, making the effective stress the same as the nominal stress.
However, if field data is collected the partial load factor can reduce the nominal
stress by as much as 15%. This reduction removes the factor of safety in the
AASHTO design calculations, because there is little uncertainty in nominal stress
produced by actual data (Chotickai and Bowman, 2006). Substituting Equation
5.8 into 5.7 gives:
(£f)max = 2f?s(AF)n 5.9
39


The detail categories relevant to the 80 span are B, C, C, and E, with fatigue
thresholds of 16 ksi, 10 ksi, 12 ksi, and 4.5 ksi respectively. Only two detail
categories are used for the 95 span, B and E, with 16 ksi, and 2.6 ksi fatigue
thresholds. After solving for the maximum stress for each detail, the maximum
stress is checked against the fatigue threshold to determine if the detail section
has infinite life or needs to be checked for finite fatigue life. The only detail
categories that did not have infinite life were E for the 80 span, and E for the 95
span. Refer to Tables 5.1 and 5.2 below for the data for the determination of
infinite fatigue life on the bottom girder of the 80 span. Refer to Appendix C and
D for complete details on the top and bottom flanges of the 80 and 95 spans.
40


Span No. Dist From Support Location Type Win3) S(in3) +M (k-ft) -M (k-ft) Positive Top M Stress Bot Negative Top M Stress Bot Stress Top Range Bot (AfU=g Top VuStRng Bot Afma,=2 Top Rs(Af)eff Bot
1 12.5 Stud 4101.48 619.56 544.59 -62.02 1.59 10.55 -0.18 -1.20 1.77 11.75 0.45 3.00 0.91 5.99
1 15 EOP 3832.76 879.98 629.6 -74.43 1.97 8.59 -0.23 -1.01 2.20 9.60 0.56 2.45 1.12 4.90
1 32.5 CL PL 3832.76 879.98 873.08 -161.26 2.73 11.91 -0.50 -2.20 3.24 14.10 0.83 3.60 1.65 7.19
1 50 EOP 3832.76 879.98 729.89 -248.1 2.29 9.95 -0.78 -3.38 3.06 13.34 0.78 3.40 1.56 6.80
1 65 EOP (off) 771.25 771.25 343.47 -322.53 5.34 5.34 -5.02 -5.02 10.36 10.36 2.64 2.64 5.28 5.28

1/2 0 CL PL 771.25 771.25 112.87 -476.41 1.76 1.76 -7.41 -7.41 9.17 9.17 2.34 2.34 4.68 4.68

2 15 EOP 771.25 771.25 335.65 -365.81 5.22 5.22 -5.69 -5.69 10.91 10.91 2.78 2.78 5.57 5.57
2 25.08 Stud 4101.48 619.56 593.36 -291.46 1.74 11.49 -0.85 -5.65 2.59 17.14 0.66 4.37 1.32 8.74
2 40.7 BM 4101.48 619.56 672.41 -176.25 1.97 13.02 -0.52 -3.41 2.48 16.44 0.63 4.19 1.27 8.38
2 56.33 Stud 4101.48 619.56 524.08 -285.25 1.53 10.15 -0.83 -5.52 2.37 15.68 0.60 4.00 1.21 7.99
2 65 EOP 771.25 771.25 316.68 -346.5 4.93 4.93 -5.39 -5.39 10.32 10.32 2.63 2.63 5.26 5.26

2/3 0 CL PL 771.25 771.25 113.46 -463.6 1.77 1.77 -7.21 -7.21 8.98 8.98 2.29 2.29 4.58 4.58

3 15 EOP (off) 771.25 771.25 356.86 -346.5 5.55 5.55 -5.39 -5.39 10.94 10.94 2.79 2.79 5.58 5.58
3 30 EOP 3832.76 879.98 786.23 -266.54 2.46 10.72 -0.83 -3.63 3.30 14.36 0.84 3.66 1.68 7.32
3 47.5 CL PL 3832.76 879.98 803.9 -173.25 2.52 10.96 -0.54 -2.36 3.06 13.33 0.78 3.40 1.56 6.80
3 65 EOP 3832.76 879.98 650.53 -79.96 2.04 8.87 -0.25 -1.09 2.29 9.96 0.58 2.54 1.17 5.08
Table 5.1 80 Span Girder Stress Distribution


Table 5.2 80 Span Girder Bottom Flange Fatigue Life Check
Span No. Dist From Support Location Type Detail Cat Af AFth Result
1 12.5 Stud B 5.99 16 Infinite
1 15 EOP E 4.90 4.5 CHECK
1 32.5 CL PL B 7.19 16 Infinite
1 50 EOP E 5.80 4.5 CHECK
1 65 EOP (off) E 5.28 4.5 CHECK

1/2 0 CL PL C 4.58 12 Infinite

2 15 EOP E 5.57 4.5 CHECK
2 25.08 Stud B 8.74 16 Infinite
2 40.7 BM B 8.38 16 Infinite
2 55.33 Stud B 7.99 16 Infinite
2 65 EOP E 5.25 4.5 CHECK

2/3 0 CL PL C 4.58 12 Infinite

3 15 EOP (off) E 5.58 4.5 CHECK
3 30 EOP E 7.32 4.5 CHECK
3 47.5 CL PL B 5.80 16 Infinite
3 65 EOP E 5.08 4.5 CHECK
5.3.4 Finite Fatigue Life
From the infinite fatigue life check in section 5.3.3, it was determined that all E
and E detail categories for the 80 and 95 spans need to be checked for finite
fatigue life. For the case of the Evans Bridge, detail category E and E both
occur at the end of the partial length cover plates, but there is a difference in the
flange thickness of the girders. The 80 span girder is a W36x135 with a flange
thickness of 0.79 inches, and the 95 span girder is a W36x182 with a flange
thickness of 1.18 inches. For a partial length cover plate, the detail category
changes from E to E when the flange thickness of the W shape is greater than
0.8 inches.
Finite fatigue life is derived from the equation used for design of fatigue
resistance, in which the nominal stress is a function of the detail category
constant, A, over the number of cycles, N, that will cause the detail to fail due to
42


fatigue. Equations 5.10 through 5.13 derive the design equation to calculate how
many years, Y, the detail will last before failure.
(AF)n
5.10
Where:
N = 36SYn(ADTT)SL
5.11
Where:
n = Cycles per Truck Passage (LRFD, 2012, pg. 6-51)
Substituting Equation 5.11 into Equation 5.10 gives:
(AF)n =
Vs
\.365Yn(ADTT)SL>
5.12
Solving for the number of years, Y, gives:
Y =
A
365n(ADTT)SL&F)n3
5.13
43


The AASHTO Manual for Bridge Evaluation uses Equation 5.13 with two
modifications to determine the finite fatigue life. First, the effective stress is used
in lieu the nominal stress, which per Equation 5.8 is the nominal resistance
multiplied by the partial load factor. When designing versus evaluating a bridge
from collected data, the partial load factor is 1.0, making the effective stress the
same as the nominal stress. The second modification is the multiplication of the
constant A by the resistance factor, Rr, which is dependent upon the detail
category. There are three levels for the resistance factor: the minimum fatigue
life, the evaluation fatigue life, and the mean fatigue life. For all minimum fatigue
life, the resistance factor equals 1.0, which is the resistance for design. Equation
5.14 shows Equation 5.13 with the partial load and resistance factors. Both the
partial load factor and the resistance factor will increase the number of years a
structural member will last when evaluating members for fatigue life, due to that
collected data of how the member is actually responding will provide more
accurate results and factors of safety can be reduced.
Y =---------------------- 5.14
365n(ADTT)sLlRs(AF)n]3
Since the bridge being evaluated for fatigue life and not being designed, the
resistance factor, Rr, for the minimum, evaluation, and mean are considered.
Using Equation 5.14 the design fatigue life can be determined from the traffic
counts and nominal stress with varying fatigue resistance. Tables 5.3 and 5.4
below show the minimum, evaluation, and mean fatigue lives for the bottom
44


flange of the 80 and 95 spans. From these calculations the minimum that the 80
span girder would last is 48 years, whereas the mean life gives the girder 77
years. The 95 span has a minimum fatigue life of 25 years (which is not possible
since the bridge is already 40 years old), and the mean fatigue life is calculated
at 63 years. Refer to Appendix C and D for more details.
Table 5.3 80 Span Girder Bottom Flange Fatigue Life
Span No. Dist From Support Location Type Detail Cat Result A (ksi3) Afeff Yrrln Rr-1 Yeval RR=Varies Ymean RR=Varies
1 12.5 Stud B Infinite 1.20E+10 3.00 N/A N/A N/A
1 15 EOP E CHECK 1.10E+09 2.45 160 208 256
1 32.5 CL PL B Infinite 1.20E+10 3.60 N/A N/A N/A
1 50 EOP E CHECK 1.10E+09 3.40 60 78 95
1 65 EOP (off) E CHECK 1.10E+09 2.64 127 165 204

1/2 0 CL PL C' Infinite 4.40E+09 2.34 N/A N/A N/A

2 15 EOP E CHECK 1.10E+09 2.78 109 142 174
2 25.08 Stud B Infinite 1.20E+10 4.37 N/A N/A N/A
2 40.7 BM B Infinite 1.20E+10 4.19 N/A N/A N/A
2 56.33 Stud B Infinite 1.20E+10 4.00 N/A N/A N/A
2 65 EOP E CHECK 1.10E+09 2.63 129 167 206

2/3 0 CL PL C' Infinite 4.40E+09 2.29 N/A N/A N/A

3 15 EOP (off) E CHECK 1.10E+09 2.79 108 140 173
3 30 EOP E CHECK 1.10E+09 3.66 48 62 77
3 47.5 CL PL B Infinite 1.20E+10 3.40 N/A N/A N/A
3 65 EOP E CHECK 1.10E+09 2.54 143 186 229
Table 5.4 95 Span Girder Bottom Flange Fatigue Life
Span No. Dist From Support Location Type Detail Cat Result A (ksi3) Afrff Ymin Rr=1 RR=Varies Ymean RR=Varies
4 16 EOP E1 CHECK 3.90E+08 2.16 105 168 262
4 38.5 CL PL B Infinite 1.20E+10 3.50 N/A N/A N/A
4 61 EOP E1 CHECK 3.90E+08 3.27 30 48 75
4 80 EOP (off) E1 CHECK 3.90E+08 2.21 97 156 244

4/5 0 CL PL B Infinite 1.20E+10 2.06 N/A N/A N/A

5 15 EOP E1 CHECK 3.90E+08 2.26 91 146 228
5 48.4 BM B Infinite 1.20E+10 3.79 N/A N/A N/A
5 80 EOP E1 CHECK 3.90E+08 2.12 111 177 277

5/6 0 CL PL B Infinite 1.20E+10 1.99 N/A N/A N/A

6 15 EOP (off) E1 CHECK 3.90E+08 2.35 81 130 203
6 34 EOP E1 CHECK 3.90E+08 3.48 25 40 63
6 56.5 CL PL B Infinite 1.20E+10 3.34 N/A N/A N/A
6 79 EOP E1 CHECK 3.90E+08 2.26 92 147 230
45


6. Strain Transducer Testing Procedures
6.1 Strain Transducer History
Hunter Christie originally developed the Wheatstone bridge circuit in 1833,
although Charles Wheatstone popularized the circuit, which is why the circuit was
named the Wheatstone Bridge (Stefanescu, 2011). The Wheatstone Bridge
circuit utilizes the force applied to change the voltage of the circuit which is then
calculated back into force for the data output (Desai, 2007). Strain transducers
were developed due to the simplicity and sensitivity of this circuit configuration.
The pile driving industry began using Wheatstone Bridge circuit strain
transducers to record the strains of the piles in 1970 (BDI Operations Manual,
2011)
6.2 Strain Transducer Development
Bridge Diagnostics Incorporated (BDI) has further developed the strain
transducer used by the pile driving industry, BDI Strain Transducer ST350, to
collect data for dynamic and event driven stresses of bridge and building
structural members through means of nondestructive testing, shown in Figure
6.1. The mounting of the transducers to steel uses an adhesive, making the
process entirely nondestructive. The transducer are built to be a manageable
size and fairly inconspicuous, measuring 4.35 inches (110.5 mm) long by 1.23
inches (31.2 mm) wide and .51 inches (13 mm) thick.
46


The ST350 transducers have a flexible design so that large strains can be
measured from the structural member without placing much axial load on the
transducer. Only live load strains are recorded, since the dead load is a static
load rather than a dynamic load. The dynamic strain data from an event occurs
in such a short time frame that thermal movements of the structural member and
transducer are assumed to be negligible.
6.3 Transducer Installation
On March 8, 2011, BDI installed 20 ST350 strain transducers to the bottom
flanges of the steel girders on spans 1 and 2 of the west end of the Evans
Bridge, shown in Figure 6.2. FHU predetermined that the fatigue prone locations
in the girders are at the ends of the partial length cover plates and installed the
47


transducers within 4 >2 inches of the ends of the cover plates, as shown in Figure
6.3.
Figure 6.2 Strain Transducer Locations (Felsburg et al, 2011)
48


Figure 6.3 Transducer Location to Partial Cover Plate
(Felsburg et al, 2011)
Since the strain needed to be read for the span of the beam and the bottom of
the girder was accessible, the transducers were aligned parallel to the length of
the girder and positioned in the center of the flange 4 % inches from the ends of
the partial length cover plates, as shown in Figure 6.3. Dirt, paint, oxidation, and
any other contaminants were removed by lightly grinding the surface before
installation to guarantee adhesion of the transducer. Guidelines were then drawn
on the mounting surface for accurate alignment, as the transducer will only read
strain in the axis in which it is aligned. Measurements were taken to the center of
the flange and marked where the center of the transducer should be. Small lines
were then marked perpendicular to the length of the girder 1% inches on either
side of the transducer midpoint. These marks indicated the center of the bolt
holes. To ensure proper alignment of the transducer bolt holes to the marks on
the girder, the transducer tab bolts were first placed through the transducer and
the nuts tightened prior to adhering the tabs to the steel.
49


Once the tabs were mounted to the transducer, a small amount of adhesive
was applied to the bottom of the tabs. The tabs, with the transducer attached,
were then placed onto the locations previously marked on the steel and removed.
In this step, some of the adhesive was placed onto the girder, and then a small
amount of adhesive accelerator was sprayed onto the adhesive left on the steel
while the transducer and tabs were mounted to the same location as previously
placed. The adhesive accelerator reduces the amount of human error in the
alignment of the system as the transducer only needs to be held in place for 15-
20 seconds for adhesion. The final process included aluminum covers with a
foam board insulation being mounted around each transducer to protect the
system while monitoring the bridge, as seen in Figure 6.4 and Figure 6.5.
50


Figure 6.5 14 of 20 Installed Transducers
BDIs transducers are all prewired and quickly connect to their structural
monitoring system where the data is recorded. The structural monitoring system
was mounted to the steel channels above the concrete piers using clamps to
ensure an entirely nondestructive testing system, shown in Figure 6.6. A lock
box containing a 12-volt battery providing power to the monitoring system was
mounted to the steel in a similar manner as the monitoring system, shown in
Figure 6.7. BDI collected the data logged by the monitoring system wirelessly on
a cell phone and downloaded the strain readings regularly to the office computer
system.
51


Figure 6.6 Structural Monitoring System
Figure 6.7 Structural Monitoring System Power Source
52


6.4 Transducer Removal
On April 12, 2011, BDI removed the ST350 strain transducers and the
supporting system from the Evans Bridge. The order of the removal process is
important to keep the transducers from being damaged and useful for further
projects. Prior to removing the transducers, the aluminum cover was removed.
During installation the adhesive tabs were mounted to the transducers first and
then mounted to the girders to ensure accuracy of placement. However, during
disassembly the transducers were first removed from the tabs prior to removing
the tabs from the steel. After the transducers and tabs were removed, the
monitoring system including the battery and housing boxes were removed. The
disassembly of the system was quick, taking approximately an hour to complete.
53


7. Strain Transducer Results and Analysis
7.1 Traffic Counts
7.1.1 Traffic Data
BDI took traffic counts March 8, 2011 through March 25, 2011, while also
collecting data from the strain transducers placed on the girders of the Evans
Bridge. These supplemental traffic counts were collected to verify the counts
collected for the 2009 Condition Inspection Report. The data collected was
separated into the following categories: bikes, cars/trailers, two-axle four tire
trucks, buses, two-axle six tire trucks, three-axle single-unit trucks, four-axle
single-unit trucks, five-axle single-unit trucks, five-axle double-unit trucks, six-axle
double-unit trucks and larger, anything smaller than six-axle multi-unit trucks, and
six-axle multi-unit trucks.
The largest recorded total traffic count of those days was Friday, March 11,
2011, with a total 16,009 vehicles and 1,480 vehicles larger than two-axle four
tire trucks. This was not the highest truck count as that number was exceeded
on four consecutive days from Tuesday, March 15, 2011, through Friday, March
18, 2011, with counts of 1,535, 1,536, 1,495, and 1,498, respectively.
Considering the timing of these counts there could be correlation in the increase
in truck traffic to the amount of alcohol distribution for Saint Patricks Day holiday
and the following weekend. Refer to Appendix E for more data on the traffic
counts collected by BDI.
54


7.1.2 Average Daily Truck Traffic
Average Daily Truck Traffic (ADTT) is utilized in calculating the fatigue life of
a bridge. From the 2009 Condition Inspection Report the ADTT was 1,510 trucks
per day in one direction. In order to verify the accuracy of the previous counts,
BDI collected additional traffic counts referenced in 7.1.1. The three highest
consecutive days of truck traffic to calculate the ADTT were 1,535, 1,536, and
1,495, averaging 1,522 trucks per day in one direction. For consistency, it was
assumed that the count of 1,522 trucks was close enough to utilize the same
ADTT of 1,510 trucks used in the 2009 Condition Inspection Report.
7.2 Control Test
7.2.1 Control Test
On March 24, 2011, between 6:30 AM and 7:00 AM, a control test was
conducted on the Evans Bridge. A tandem axle loaded truck of known weight,
51,560 lbs, was driven across the bridge while all other traffic on Evans was
stopped on either side of the ramps leading up to the bridge and the traffic on
Santa Fe Drive was diverted to the next exit (refer to Figure 7.1 through Figure
7.4). The purpose of this test was to determine how much a single truck would
stress the bridge girders.
55


Figure 7.1 Truck at Base of Evans Bridge for Control Test
Figure 7.2 Truck Climbing Ramp of Evans Bridge for Control Test
56


Figure 7.3 Truck Approaching Strain Transducers During Control Test
Figure 7.4 Truck Completing Control Test
Four passes were completed with the truck, all of which were completed in
the eastbound direction over the bridge above the strain transducers. The truck
57


was at a slow crawl speed in each lane for two of the tests, and then a high-
speed test was completed in each lane as well. During these tests the structural
monitoring system was set up to record event data.
7.2.2 Control Test Results
Event data was recorded for each of the four control tests with the structural
monitoring system recording the stress of each transducer at 0.02 second
intervals. For each one-second of time, 50 data points were documented for each
transducer. Each test logged anywhere from 60,000 to 80,000 data points, which
can be difficult to evaluate, but plotting the points provided a good visual
representation of what occurred during the tests.
As the truck passed over the transducers, tension (shown as positive) was
always read first since the bending moment is placing the bottom flange of the
girder in tension. Once the truck passed and the girder reverberated back into its
original shape, the bottom flange of the girder went into compression (shown as
negative). Although the magnitude of the compressive stress was less than that
of the tensile stress, it was still a noticeable force.
58


During Test 1 the truck was at a crawl speed in the exterior lane and at
approximately 28 seconds into the test the transducers began to record stresses
beyond the normal vibrations of the bridge. Transducer J1 recorded the
maximum stress of 3.68 ksi tension before recoiling into 1.02 ksi of compression.
The tension and compression stresses at transducer J1 have the maximum
stress range for Test 1 of 4.71 ksi; refer to Figure 7.5 for the plot of Test 1
transducers F1 through K1.
Figure 7.5 Control Test 1 Results for Transducers F1-K1
59


During Test 2 the truck was also at a slow speed, but drove in the interior
eastbound lane. The maximum stress range of 4.42 ksi occurred at transducer
11, with the maximum tensile stress of 3.53 ksi, and the maximum compressive
stress of 0.89 ksi. Refer to Figure 7.6 for the plot of Test 2 for transducers F1
through K1.
Figure 7.6 Control Test 2 Results for Transducers F1-K1
60


The third test was completed in the interior eastbound lane at a high-speed,
relative to the speed limit. Similar to Test 2, which was also completed in the
interior lane, Transducer 11 had the maximum recorded stress range of 4.35 ksi,
where 3.36 ksi was in tension and 0.99 ksi was in compression. See Figure 7.7
below for the plot of Test 3 for transducers F1 through J1.
Figure 7.7 Control Test 3 Results for Transducers F1-K1
61


Test 4 was completed in the exterior lane at a high speed. Transducer J1
reached a tensile stress of 3.55 ksi and a compressive stress of 0.95, with the
maximum stress range of 4.50 ksi. These findings were consistent with those of
Test 1, which was also conducted in the exterior eastbound lane. Refer to Figure
7.8 for the plotted results of Test 4. Test results for the four control tests are
summarized in Table 7.1.
Figure 7.8 Control Test 4 Results for Transducers F1-K1
62


Table 7.1 Control Test Results Summary
Tesion (ksi) Compression (ksi) Maximum Stress Range (ksi) Transducer
Control Test 1 3.68 1.02 4.70 J1
2 3.53 0.89 4.42 11
3 3.36 0.99 4.35 11
4 3.55 0.95 4.50 J1
All four of the tests resulted in a stress range within 0.2 ksi of the 4.5 ksi
threshold of the 80 span girders. Since the speed of the truck did not seem to
have an affect on the stress recorded by the transducers, the overall weight of
the loaded truck was determined as the cause of the stress range reaching the
threshold. From these findings it can be concluded that an unloaded tandem
truck would not produce these values; therefore it is the passage of loaded trucks
that will affect the girder fatigue life.
The control test also proves the number of cycles per passage, n, of a truck.
For a 3-span continuous girder longer than 40 there are two values for n, near
an interior support and elsewhere. The strain transducers were installed near the
center of the first bay. Based on Figures 7.5 through 7.8, the number of cycles
read by each truck passage was one, where the peak of the tension to the peak
of the compression stresses is read as one cycle. This is consistent with
AASFITO stating n=1.0 for anywhere in multiple span girders that is not adjacent
to an interior support.
63


7.3 Stress Cycles
7.3.1 Stress Cycle Counts
BDI collected strain data from March 8, 2011, through April 11,2011. The
structural monitoring system was programmed to record the number of stress
cycles per hour that ranged between 1 ksi and 11 ksi in .5 ksi increments, and
stress cycles greater than 11 ksi (refer to Table 7.2). These stress ranges
correlate to the ranges the transducer reaches during a cycle, not the actual
stress reached. For example, during a cycle the transducer could read -2 ksi and
3 ksi, this would place the cycle within the 5 ksi range. The stress cycles were
recorded and logged separately for each of the 20 strain transducers. From the
40,516,236 cycles recorded, 97.1% occurred within the 1 ksi to 1.5 ksi range.
64


Bin Range, ksi
1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0 4.0-4.5 4.5-5.0 5.0-5.5 5.5-6.0 6.0-6.5 6.5-7.0 7.0-7.5 7.5-8.0 8.0-8.5 8.5-9.0 9.0-9.5 9.5-10.0 10.0-10.5 10.5-11.0 >11
FI 1778530 53793 9048 4072 1578 969 617 290 95 35 35 11 7 1 1 0 0 0 0 0 0
G1 2229302 85524 11380 4226 3240 1789 643 295 267 250 193 89 51 23 14 9 7 4 2 1 1
Glcp 1543112 30954 6231 2381 532 444 233 70 20 15 2 2 1 0 0 0 0 0 0 0 0
HI 2227484 60951 8426 4127 1373 702 429 246 91 55 20 10 2 5 3 0 0 0 0 0 0
11 2115270 80631 9238 2198 1289 759 304 174 91 65 40 15 10 6 2 1 0 0 0 0 0
J1 2501792 90676 7790 2073 792 379 183 121 165 103 35 12 8 2 3 0 3 0 0 0 0
K1 2340077 83308 4558 1100 428 173 85 150 139 33 10 3 3 2 3 0 0 0 0 0 0
c F2 1610275 34537 6873 2189 823 463 153 31 8 3 1 1 0 0 0 0 0 0 0 0 0
o G2 1797064 38970 5762 3477 756 337 390 150 30 13 6 4 2 0 0 0 0 0 0 0 0
ec G2cp 1633211 16079 3285 658 289 31 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
"ti H2 1718024 46096 7265 2639 787 519 161 60 15 8 0 0 0 0 0 0 0 0 0 0 0
ra 12 1774871 57845 4151 1465 732 214 134 70 23 12 1 0 0 0 0 0 0 0 0 0 0
J2 2689451 50577 3582 890 300 211 178 32 10 1 0 3 0 0 0 0 0 0 0 0 0
K2 2480656 30555 1942 532 155 246 88 11 1 2 2 0 0 0 0 0 0 0 0 0 0
F3 2151529 35011 5809 1700 673 168 58 14 1 1 0 0 0 0 0 0 0 0 0 0 0
G3 1665554 37545 6964 2915 856 460 247 69 24 14 2 1 0 0 0 0 0 0 0 0 0
H3 1611747 39881 6580 1805 753 375 133 45 15 5 1 0 0 0 0 0 0 0 0 0 0
13 1880753 40014 3648 1354 511 205 104 24 8 5 0 0 0 0 0 0 0 0 0 0 0
J3 1502862 36993 3038 765 265 235 98 32 3 5 0 0 0 0 0 0 0 0 0 0 0
K3 2097111 25691 1685 409 129 206 101 10 5 1 0 0 0 0 0 0 0 0 0 0 0
Table 7.2 Stress Cycle Count Summary


As previously discussed in 5.3.4, the fatigue threshold for a beam with a
flange less than 0.8 inches at the end of a cover plate is 4.5 ksi (AASHTO, 2012).
During the testing, 4,211 stress cycles were recorded over the 4.5 ksi threshold,
equaling 0.01 % of the total counted cycles.
Only once did the monitoring system record a stress cycle over 11 ksi which
occurred on March 31,2011, between 10:00 and 11:00a.m. and was recorded on
transducer G1 (refer to figure 7.9). Transducer G1 was located on the first span
approximately 50 feet from the west end, and the girder is located in the center of
the bridge.
66


Figure 7.9 Strain Transducer Locations
(Felsburg et al, 2011)
7.3.2 Stress Cycle Data Analysis for 80 Girder Span
The data collected was first totaled into the number of times each strain
transducers reached a specific stress range, 1 ksi to 1.5 ksi, 1.5 ksi to 2 ksi, etc.,
during the 31 day data collection period; refer to Table 7.2 and Appendix F for a
summary. After the data was organized into a more manageable way, the data
was totaled again in two separate manners. The first was the total of the cycle
67


counts for a particular stress range. In this model 1 ksi to 1.5 ksi, 1.5 ksi to 2 ksi,
etc., were calculated, disregarding the specific transducer correlated to the count
From the total cycle counts per stress range the percentage of occurrences over
the 4.5 ksi threshold were calculated. In the second method the number of
occurrences for a specific transducer was totaled, disregarding the particular
stress range that the stress cycle occurred in. The total cycle count per
transducer was used to calculate the percentage of cycles at a particular stress
range, which provides y,.
Estimating the finite fatigue life of an element, as discussed in section 5.3.4,
is a function of the detail category constant, A, the average number of trucks in
one direction per day in a single lane, (ADTT)sl, and the effective fatigue
threshold, (Af)eff, refer to Equation 7.1 (AASHTO, 2011). Previously determined,
the detail category for a W36x135 at the end of a partial length cover plate is E,
giving the constant, A, of 11x108 ksi3 (AASHTO, 2012).
Y _________RrA_______ j -|
365nC4D7T)si[(A/)e//]3
Where:
Y = Number of Years of a Structural Element Due to Fatigue
Rr = Resistance Factor for Minimum Fatigue Life
n = Number of Stress Range Cycles per Truck Passage
68


Solving for the finite fatigue life of the girders, Rr is set as 1.0 for the
minimum life for all detail categories, which will produce the most conservative
evaluation, because it is assuming a 2% probability of failure. The number of
stress range cycles per truck passage, n, was taken as 1.0 since the transducers
were located in the middle of the girder span girder and not near a support.
(ADTT)sl is the average daily truck traffic in a single lane, which is the product of
the ADTTcount, and the number of lanes available to trucks in one direction, p
(AASHTO, 2012). Each direction of the Evans Bridge has two lanes available to
trucks; therefore, p is 0.85. Using the ADTT of 1,510 as previously determined,
(ADTT)sl is calculated at 1,284 trucks in one lane per day.
After determining the (ADTT)sl, only one variable remains in estimating the
finite fatigue life of one of the girders, the effective stress, (Af)etf. In the collected
data, the effective stress is determined from the particular stress range, Afh and
the percentage of cycles at the particular stress range, yv, Equation 7.2
(AASHTO, 2011). The percentage of cycles at a particular stress range for a
specific transducer were determined from the number of cycles that occurred
within a stress range over the total cycles counted for the transducer; refer to
Appendix F. For the particular stress range, the value was taken as the
maximum of the predetermined range- for example, a stress range of 1.5 ksi to 2
ksi would use a Afj of 2 ksi. Assuming all particular stress ranges are at the
maximum end of the range, more conservative results will be produced. More
accurate results would be produced if smaller stress ranges were programmed
into the structural monitoring system; however, this would create more data
69


points and create a more intensive analysis. Since the fatigue life calculation is
only an estimate, it is reasonable to have stress cycle ranges with 0.5 ksi
increments.
(A Heff = Rs(ZyM3)1/3 7.2
Where:
Rs = Stress-Range Estimate Partial Load Factor
The Stress-Range Estimate Partial Load Factor, Rs, can be taken as 0.85,
since the fatigue life evaluation is using stress ranges collected from field-
measured strains (AASHTO, 2011). This reduction removes the factor of safety
in the AASHTO design calculations, because there is little uncertainty in nominal
stress produced by actual data (Chotickai and Bowman, 2006). The partial load
factor can be taken for both the minimum and evaluation fatigue life calculations.
Calculating the mean fatigue life for all scenarios requires the partial load factor
to be 1.0, which will decrease the amount of years compared to that of the
minimum and evaluation fatigue lives. However, the resistance factor, Rr,
applied in equation 7.1 allows an increase for the mean fatigue life for detail
category E of 1.6. As discussed in 5.3.4, this factor accounts for the evaluation
fatigue life being one standard deviation below the mean and the minimum
fatigue life being two standard deviations below the mean.
Anywhere from 95% to 99% of the recorded stress cycles for each transducer
occurred between 1 ksi and 1.5 ksi. The high percentage of low stress cycle
70


occurrences skews the estimated fatigue life of the bridge. When using the 1 to
1.5 ksi stress range, the calculations estimate that one girder would last 982
years (refer to Table 7.3 and Appendix F for more information). This does not
provide an accurate estimate of the actual finite fatigue life of a girder, as actual
fatigue failure is a specific number of cycles that occur over the girders fatigue
threshold, and the estimated fatigue life provided by AASHTO is using a
percentage of the cycles measured to calculate that number in terms of years.
Table 7.3 Estimated Minimum Finite Life of 80 Span Girders with Minimum
Stress Range of 1.0 ksi to 1.5 ksi
(IViAf3)173 Afeff Y
FI 1.55 1.32 1017
G1 1.57 1.34 982
Glcp 1.53 1.30 1061
HI 1.54 1.31 1040
11 1.55 1.32 1031
J1 1.54 1.31 1047
K1 1.53 1.30 1060
F2 1.53 1.30 1061
G2 1.54 1.30 1057
G2cp 1.51 1.29 1104
H2 1.54 1.31 1053
12 1.53 1.30 1060
J2 1.52 1.29 1092
K2 1.51 1.29 1105
F3 1.52 1.29 1086
G3 1.54 1.31 1054
H3 1.53 1.30 1060
13 1.52 1.29 1081
J3 1.53 1.30 1078
K3 1.51 1.29 1105
From the ADTT counts for the eastbound lanes, the total number of vehicles
counted from March 9, 2011 through March 24, 2011 was 228,290, 18,495 of
which were trucks. The average number of stress cycles read by all the
transducers during those 16 days was 848,365. This calculates to approximately
71


3.7 stress cycles per vehicle. The control test provided proof that only one cycle
occurred for each passing truck; therefore incorporating more stress cycles than
vehicles in the evaluation of fatigue life is inaccurate. These additional cycles
can be attributed to dynamic affects of the bridge, and if incorporated into the
fatigue life calculation, skew the remaining fatigue life calculation in an un-
conservative manner, as show above in Table 7.3. By ignoring low stress cycles,
the effective stress value increases, reducing the estimated fatigue life. Making it
conservative to ignore low stress cycles. Determining the appropriate stress
cycles to ignore or consider involves engineering judgment, however can be
compared to the controlled load test for validity.
Each individual vehicle is not likely to produce its own stress cycle, as
multiple vehicles are on the road at the same time, especially during times of
high traffic volumes. Considering this, the number of overall stress cycles would
decrease, but the stress cycle ranges would increase due to additional load of
multiple vehicles. Of the total counted cycles 820,134 (97%) occurred in the 1
ksi to 1.5 ksi range, while 23,432 (2.8%) occurred in the 1.5 ksi to 2.0 ksi range.
Ignoring stress levels from these two ranges leaves 4,827 cycles, which recorded
stresses above 2 ksi. The controlled test truck weighed 51,560 pounds and
induced a maximum stress cycle of 4.7 ksi. It is reasonable to assume events
inducing stress cycles greater than 2 ksi are capturing an event which is not
merely dynamic effects within the bridge, but are loaded trucks or combinations
of vehicles and should be considered in the fatigue life calculation.
72


With the removal of all cycles occurring below 2 ksi the minimum fatigue life
of 97 years is calculated for girder G, as shown in Table 7.4.
Table 7.4 Estimated Minimum Finite Life of 80 Span Girders with Minimum
Stress Range of 2.0 ksi to 2.5 ksi
CO \ CO < >- ksi Afeff Y
FI 3.13 2.66 125
G1 3.40 2.89 97
Glcp 2.93 2.49 151
HI 3.09 2.63 129
11 3.07 2.61 132
J1 3.08 2.62 131
K1 3.08 2.62 131
F2 2.88 2.45 160
G2 3.03 2.58 137
G2cp 2.70 2.30 194
H2 2.90 2.46 157
12 2.96 2.52 147
J2 2.92 2.48 154
K2 2.96 2.52 147
F3 2.79 2.37 175
G3 2.94 2.50 151
H3 2.87 2.44 162
13 2.90 2.47 156
J3 2.91 2.47 156
K3 2.98 2.54 144
The minimum fatigue life calculated from the transducer data is 97 years as
shown in Table 7.4. As previously stated, the minimum fatigue life uses a 0.85
partial load factor, Rs, as does the evaluation life. This is due to the estimated
stress range coming from actual data collected. However, the MBE requires all
mean fatigue life evaluations to use a partial load factor of 1.0 for all scenarios.
The resistance factor, Rr, for the minimum fatigue life of detail category E is 1.0,
whereas, the evaluation life resistance factor is 1.3, and the mean fatigue life
resistance factor is 1.6. Because the partial load factor and the resistance factor
73


differ for minimum, evaluation, and mean fatigue life calculations, Tables 7.5 and
7.6 have been included to display the effects of the load factors.
Table 7.5
Estimated Evaluation Fatigue Life of 80 Span Girders with
Minimum Stress Range of 2.0 ksi to 2.5 ksi
(ZViAf;3) 1/3 Afeff Y
FI 2.66 2.66 162
G1 2.89 2.89 126
Glcp 2.49 2.49 197
HI 2.63 2.63 168
11 2.61 2.61 171
J1 2.62 2.62 171
K1 2.62 2.62 170
F2 2.45 2.45 208
40 G2 2.58 2.58 179
ra G2cp 2.30 2.30 252
_i H2 2.46 2.46 205
CUO ru 12 2.52 2.52 191
12 2.48 2.48 200
K2 2.52 2.52 191
F3 2.37 2.37 228
G3 2.50 2.50 196
H3 2.44 2.44 210
13 2.47 2.47 203
J3 2.47 2.47 202
K3 2.54 2.54 187
74


Table 7.6 Estimated Mean Fatigue Life of 80 Span Girders with Minimum
Stress Range of 2.0 ksi to 2.5 ksi
(ZViAf3)173 Afeff Y
FI 3.13 3.13 122
G1 3.40 3.40 95
Glcp 2.93 2.93 149
HI 3.09 3.09 127
11 3.07 3.07 129
J1 3.08 3.08 129
K1 3.08 3.08 129
F2 2.88 2.88 157
G2 3.03 3.03 135
G2cp 2.70 2.70 190
H2 2.90 2.90 155
12 2.96 2.96 144
12 2.92 2.92 151
K2 2.96 2.96 144
F3 2.79 2.79 172
G3 2.94 2.94 148
H3 2.87 2.87 159
13 2.90 2.90 153
J3 2.91 2.91 153
K3 2.98 2.98 141
From the calculated fatigue lives, the minimum and mean fatigue lives are
estimated to be 97 years and 95 years respectively. The evaluation fatigue life is
estimated to be 126 years. Conservatively, the fatigue life of the 80 span girders
is 95 years; however, the girders are currently under evaluation and not design,
so it is reasonable to assume the fatigue life of the 80 span girders to be 126
years.
7.3.3. Stress Cycle Data Analysis for 95 Girder Span
Average daily truck traffic, ADTT, was used as the maximum recorded during
the 2009 counts, which was 1,189 trucks per day for the 95 span sections, since
additional counts were not conducted during the 2011 analysis. The number of
75


lanes available to trucks is two, which is constant across the bridge giving the
average daily truck traffic in a single lane, (ADTT)sl, of 1,011 trucks.
The ends of the partial cover plates are located 15 feet from the support,
which is 16% of the total span length. In order to consider the location near the
support, the distance away from the support should be 1/10 (or 10%) of the span
length (AASHTO, 2012), which will affect the number of stress cycles per truck
passage. As the end of the partial length cover plate is located within 16% of the
span length, the detail being analyzed is not close enough to be considered close
to the support and an n of 1.0 will be used in determining fatigue life.
As discussed in section 5.3.4, the girder used in the 95 span regions is a
W36x182, with a flange thickness of 1.18 inches, which places the girders in
detail category E for determining the fatigue life at the ends of the partial length
cover plates (AASHTO, 2012, pg. 6-37). Detail category E has a fatigue
threshold, (AF)th, of 2.6 ksi, and a detail category constant, A, of 3.9x108 ksi3.
Due to the girders being category E, the resistance factor, Rr, is 1.0, 1.6, and
2.5, for the minimum, evaluation, and mean fatigue life respectively.
Transducers were only placed on the first and second spans of the 80 girder
spans, and none were placed on the 95 girder spans. From the actual data the
effective stress (Af)eff for the 80 span was at most 60% of that calculated by the
using the moments produced by the modeling software. Assuming the 95 span
responds similar to the 80 span, the effective stress for the 95 span was taken
as 70% (60% plus a 10% factor of safety) of the previously calculated effective
stress from the modeling software. However, unlike the 80 span girders, the
76


partial load factor, Rs, is 1.0 for all cases, because the stress ranges are
calculated and not from collected field-measurements.
From the stresses calculated utilizing the modeling software and LRFD
design requirements, the largest effective stress was 3.48 ksi and located 34 feet
into span 3 of the 95 girder, span 6 of overall bridge length. Taking 70% of the
previously calculated stress of 3.48 ksi, gives 2.44 ksi. Using the new effective
stress in equation 7.1 to estimate the fatigue life for the 95 span girder produces
a minimum fatigue life of 73 years. The evaluation and mean fatigue life estimate
is 117 and 183 years respectively. Refer to table 7.7 for the 95 span fatigue
results and Appendix G for more information.
77


Table 7.7 Calculated Fatigue Life for the 95 Span Girders
Span No. Dist From Support Detail Cat Afmax AF, Result A (ksi3) Afeff 70% Afeff ~ Rr=1 v^i RR=Varies RR=Varies
4 16 E' 4.32 2.6 CHECK 3.90E+08 2.16 1.51 305 489 764
4 38.5 B 7.00 16 Infinite 1.20E+10 3.50 2.45 N/A N/A N/A
4 61 E' 6.55 2.6 CHECK 3.90E+08 3.27 2.29 88 140 219
4 80 E' 4.43 2.6 CHECK 3.90E+08 2.21 1.55 284 454 710

4/5 0 B 4.13 16 Infinite 1.20E+10 2.06 1.45 N/A N/A N/A

5 15 E' 4.53 2.6 CHECK 3.90E+08 2.26 1.58 266 425 665
5 48.4 B 7.58 16 Infinite 1.20E+10 3.79 2.65 N/A N/A N/A
5 80 E' 4.24 2.6 CHECK 3.90E+08 2.12 1.48 323 517 808

5/6 0 B 3.98 16 Infinite 1.20E+10 1.99 1.39 N/A N/A N/A

6 15 E' 4.71 2.6 CHECK 3.90E+08 2.35 1.65 236 378 591
6 34 E' 6.96 2.6 CHECK 3.90E+08 3.48 2.44 73 117 183
6 56.5 B 6.68 16 Infinite 1.20E+10 3.34 2.34 N/A N/A N/A
6 79 E' 4.51 2.6 CHECK 3.90E+08 2.26 1.58 268 429 671
78


8. Results
8.1 Visual Inspection Fatigue Life Design Results
Fatigue life calculations presented in chapter 5 show that in the worst case
detail the 80 span girder will last 77 years, and the 95 span will last 63 years
based on the mean fatigue life. The present age of the Evans Bridge is 40 years
old, as it was built in 1972. Remaining fatigue life is the difference of the
calculated fatigue life less the current age of the member, since the calculated
fatigue life determines the life of the member from time of construction. Tables
8.1 and 8.2 show the remaining fatigue life of the girders based on the overall
fatigue life and current age of the bridge. The minimum the 80 span girder will
last is another 37 years and the minimum the 95 span will last is an additional 23
years from the current year of 2012, based on the mean fatigue life.
79


Table 8.1 Estimated Remaining Design Fatigue Life for 80 Span
Span No. Dist From Support Location Type Detail Cat Result II §, Y^i RR=Varies Ymean R=Varies Remaining Ymin Remaining Yevai Remaining Van
1 12.5 Stud B CHECK N/A N/A N/A N/A N/A N/A
1 15 EOP E CHECK 160 208 256 120 168 216
1 32.5 CL PL B CHECK N/A N/A N/A N/A N/A N/A
1 50 EOP E CHECK 60 78 95 20 38 55
1 65 EOP (off) E CHECK 127 165 204 87 125 164

1/2 0 CL PL C' CHECK N/A N/A N/A N/A N/A N/A

2 15 EOP E CHECK 109 142 174 69 102 134
2 25.08 Stud B CHECK N/A N/A N/A N/A N/A N/A
2 40.7 BM B CHECK N/A N/A N/A N/A N/A N/A
2 56.33 Stud B CHECK N/A N/A N/A N/A N/A N/A
2 65 EOP E CHECK 129 167 206 89 127 166

2/3 0 CL PL C' CHECK N/A N/A N/A N/A N/A N/A

3 15 EOP (off) E CHECK 108 140 173 68 100 133
3 30 EOP E CHECK 48 62 77 8 22 37
3 47.5 CL PL B CHECK N/A N/A N/A N/A N/A N/A
3 65 EOP E CHECK 143 186 229 103 146 189
Table 8.2 Estimated Remaining Design Fatigue Life for 95 Span
Span No. Dist From Support Location Type Detail Cat Result Vn Rr=1 Vi R=Varies Ymean RR=Varies Remaining Ymin Remaining Yevai Remaining Ymean
4 16 EOP E' CHECK 105 168 262 65 489 764
4 38.5 CL PL B Infinite N/A N/A N/A N/A N/A N/A
4 61 EOP E' CHECK 30 48 75 -10 8 35
4 80 EOP (off) E' CHECK 97 156 244 57 116 204

4/5 0 CL PL B Infinite N/A N/A N/A N/A N/A N/A

5 15 EOP E' CHECK 91 146 228 51 106 188
5 48.4 BM B Infinite N/A N/A N/A N/A N/A N/A
5 80 EOP E' CHECK 111 177 277 71 137 237

5/6 0 CL PL B Infinite N/A N/A N/A N/A N/A N/A

6 15 EOP (off) E' CHECK 81 130 203 41 90 163
6 34 EOP E' CHECK 25 40 63 -15 0 23
6 56.5 CL PL B Infinite N/A N/A N/A N/A N/A N/A
6 79 EOP E' CHECK 92 147 230 52 107 190
8.2 Strain Transducer Fatigue Life Results
As mentioned in section 8.2, the remaining fatigue life of the bridge is
the calculated fatigue life less the current age of 40 years. From the
80


results presented in section 7, the fatigue life of the 80 span is 126 years,
and the 95 span is 117 years based on evaluation life. Tables 8.3 and 8.4
below show the remaining fatigue life of the 80 and 95 span girders.
Based on these calculations, the 80 span has another 86 years of fatigue
life remaining, which is 49 years more than by the visual inspection results
in section 8.1. The 95 span has 54 years more than the visual inspection
calculation at a total of 77 years of fatigue life remaining.
Table 8.3 Estimated Remaining Evaluation Fatigue Life for 80 Span
Ymin v 1 eval Ymean Remaining Remaining Remaining
Rr=1 RR=Varies RR=Varies Ym, Yeval Y
FI 125 162 122 85 122 82
G1 97 126 95 57 86 55
Glcp 151 197 149 111 157 109
HI 129 168 127 89 128 87
II 132 171 129 92 131 89
J1 131 171 129 91 131 89
K1 131 170 129 91 130 89
F2 160 208 157 120 168 117
o G2 137 179 135 97 139 95
n u G2cp 194 252 190 154 212 150
_i H2 157 205 155 117 165 115
M (0 U I2 147 191 144 107 151 104
J2 154 200 151 114 160 111
K2 147 191 144 107 151 104
F3 175 228 172 135 188 132
G3 151 196 148 111 156 108
H3 162 210 159 122 170 119
I3 156 203 153 116 163 113
J3 156 202 153 116 162 113
K3 144 187 141 104 147 101
81


Table 8.4 Estimated Remaining Evaluation Fatigue Life for 95 Span
Span No. Dist From Support Location Type Detail Cat Result Ymin Rr1 Yeva, RR=Varies Ymean R=Varies Remaining Ymin Remaining YM| Remaining Ymean
4 16 EOP E' CHECK 305 489 764 265 489 764
4 38.5 CL PL B Infinite N/A N/A N/A N/A N/A N/A
4 61 EOP E' CHECK 88 140 219 48 100 179
4 80 EOP (off) E' CHECK 284 454 710 244 414 670

4/5 0 CL PL B Infinite N/A N/A N/A N/A N/A N/A

5 15 EOP E' CHECK 266 425 665 226 385 625
5 48.4 BM B Infinite N/A N/A N/A N/A N/A N/A
5 80 EOP E' CHECK 323 517 808 283 477 768

5/6 0 CL PL B Infinite N/A N/A N/A N/A N/A N/A

6 15 EOP (off) E' CHECK 236 378 591 196 338 551
6 34 EOP E' CHECK 73 117 183 33 77 143
6 56.5 CL PL B Infinite N/A N/A N/A N/A N/A N/A
6 79 EOP E' CHECK 268 429 671 228 389 631
82


9. Cost Comparison
The fatigue analysis results based off of the visual inspection would require
retrofits to extend the girder life beyond 20 years. Retrofits would be made to all
of the partial length cover plates at the bottom flanges of the girders. Each
retrofit would cost approximately $5,000 and with 12 girders this would cost
$60,000 per location. Both the 80 and 95 3-span girders have four locations
where a bottom cover plate exists, totaling approximately $720,000 to retrofit the
bottom flange cover plates. Additionally, some of the top flange cover plates
would need to be retrofitted as well. This would require removing a strip of deck
above the girder to gain access to the cover plate. The total retrofit cost was
estimated at upwards of $1,000,000.
Due to the remaining fatigue life of the girders being based on visual
inspection and ultimately the worst case scenario, CCD and FHU considered the
alternative of hiring BDI to gather actual stress data on the Evans Bridge and
recalculate the remaining fatigue life of the girders. In order to avoid retrofitting
at this time, the girders need to last a minimum of 20 additional years. The
results show that a costly retrofit is not necessary at this time, since the shortest
remaining fatigue life span was calculated at 55 years for the 80 span and 33
years for the 95 span, assuming minimum fatigue life. The cost of hiring BDI to
gather this data was $22,000, saving CCD and ultimately the taxpayers, at least
$978,000 to complete the rehabilitation project to the Evans Bridge.
83


10. Conclusions and Future Research
10.1 Conclusions
As discovered in early research, two members of the same material with the
same physical properties may have different fatigue lives because the
imperfections in the particular members are different. With this variation in
fatigue life, the finite fatigue life as determined by AASHTO, both the LRFD and
the MBE, is only an estimation of the structural members longevity. The
probability that a member will fail is dependent on whether the analysis is for
design or evaluation purposes, which places the burden of the decision heavily
on the engineer.
Engineering judgment plays a large role in determining the most likely
situation to occur regarding evaluation of fatigue life of an existing structure.
Many factors have been found to affect the variables of fatigue life and ultimately
the decision and engineer needs to make. Some are simple, such as the
remaining fatigue life is negative or zero, but with no visible cracks it is safe to
assume that determination is incorrect and use a higher probability of failure.
Other decisions regarding the most likely case of remaining fatigue life can be
difficult, such as whether or not the member will last 8 or 22 years based off of
minimum or evaluation lives. A major asset to the fatigue analyses was, and
continues to be, CCD completing biannual bridge inspections of the Evans
Bridge. The fatigue critical details can be monitored for cracking and if cracking
84


occurs, then a retrofit would be necessary to repair the girders before fatigue
failure occurs.
By collecting field measurements, such as ADTT counts and stress cycles,
the results become more accurate and fatigue life is extended which can assist in
reducing some of the questionability. An additional benefit for completing an
analysis from collected stress cycles is the amount of money saved by CCD for
the taxpayers. Completing analyses, based on both a visual inspection and the
measured stress cycles, the concluding outcome is that the data gathered by the
strain gauges produces less conservative and more realistic results.
10.2 Future Research
Much can be done to further the research presented in this thesis, and given
the subjectivity to estimating fatigue life, it should. Further investigations on ways
to reduce weld stress at fatigue critical details would do well to be researched
further, and could be beneficial to a global audience.
Additional research pertaining directly to the Evans Bridge should include
continuing to collect strain data once the rehabilitation project is complete. If long
term strain gauges were installed and monitored from the resurfacing through the
next cycle of deterioration, assessments of how the road conditions effect the
stress of the bridge could be beneficial for CCD to use in maintaining the bridges
across Denver. Another research method, which would be of local value, could
be to periodically collect traffic and strain data and reanalyze the bridge to
determine increases in traffic, increase in truck loading, and continuing to
85


estimate the remaining fatigue life of the Evans Bridge. This information can be
used to help determine what changes are occurring in the estimation and why.
Another important topic to research would be the redundancy of the steel
girders. If one girder failed, or multiple damaged, would the bridge have total
failure? Several 3-span continuous steel girder bridges, such as the Lafayette
Street Bridge in Minneapolis St. Paul, the Ontario-35 Bridge, and 1-79 Bridge
over the Ohio River, have survived total collapse after the failure of one of the
central span girders (Frangopol and Curley, 1987). A study was done on a
continuous 3-span steel girder bridge built in the late 1960s in Weathersfield, VT.
This study compared field collected strain data to a finite element analysis of the
girders following damage to three of the five girders due to an over height truck
impact (Brena et al., 2012). The three damaged girders had not failed
completely and were able to carry a reduced load. Due to the redundancy of the
girder system along with unintended composite action with the concrete deck, it
was determined that the damaged bridge was still acceptable to carry the
highway loads (Brena et al., 2012).
The case of the Evans Bridge is similar to these, in which it is a 3-span
continuous steel girder bridge. It is reasonable to assume the redundancy of the
12 girders would support the bridge if one were to fail. Studying the effects of
losing the use of a girder due to fatigue failure, on the Evans Bridge, using a
finite element analysis would be a good topic to further investigate for CCD in
order to avoid total collapse of the structure.
86


Future research needs to continue and be expanded especially due to the
variability of the subject and lack of research. Denver could be on the forefront of
developing these methodologies. By continuing research Denver could help
other municipalities across the nation implement practices to be more accurate
and save money when analyzing aging structures for fatigue life.
87


REFERENCES
Alampalli, S. & Lund, R. (2006). Estimating Fatigue Life of Bridge Components
Using Measured Strains. Journal of Bridge Engineering 11{6), 725-736.
American Association of State Highway and Transportaion Officials. (2011). The
Manual for Bridge Evaluation. (2nd ed.) Washington, DC: American
Association of State Highway and Transportation Officials.
American Association of State Highway and Transportaion Officials. (2012).
AASHTO LRFD Bridge Design Specifications. (6th ed.) Washington, DC:
American Association of State Highway and Transportation Officials.
Bowman, M., Fu, G., Zhou, Y. E., Connor, R. & Godbole, A. National Coopertive
Highway Research Program. (2012). NCHRP Report 721 Fatigue Evaluation
of Steel Bridges. Washington, DC: National Cooperative Highway Research
Program.
Brena, S., Jeffery, A. & Civjan, S. (2012, April 10). Evaluation of a Non-
composite Steel Girder Bridge through Live-load Field Testing. Journal of
Bridge Engineeringl -19.
Bridge Diagnostics Inc., (2011). 5.2 BDI Strain Transducer-ST350. Boulder, CO:
Unpublished. Retrieved from http://bridgetest.com/products/bdi-strain-
transducers/
Chotickai, P. & Bowman, M. (2006). Comparative Study of Fatigue Provisions for
the AASFITO Fatigue Guide Specifications and LRFR Manual for Evaluation.
Journal of Bridge Engineering 11 (5), 655-660.
Desai, J. (2007, October 29). Usin a Strain-Gauge Transduer in a Wheatstone
Bridge Configuration, When Deploying this Classic, Versitaile Circuit
Configuration to Measure Strain, Include a Dummy Gauge for Best Results
Electronic Engineering Times. CMP Media, Inc., 29 Oct. 2007. Retrieved from
http://www.eetimes.com/design/analog-design/4009984/Using-a-strain-
gauge-transducer-in-a-Wheatstone-bridge-configuration
Connor, R., Dexter, R. & H. National Coopertive Highway Research Program.
(2005). NCHRP Synthesis 354 Inspection and Management of Bridges with
Fracture-Critical Details. Washington, DC: National Cooperative Highway
Research Program.
88


Federal Highway Administration (n.d.). Questions and Answers on the National
Bridge Inspection Standards 23 CFR 650 subpart C Bridge Technology, n.d.
Retrieved October 3, 2012 from http://www.fhwa.dot.gov/bridge/nbis/
Felsburg, Holt, & Ullevig, & LONCO, City and County of Denver. (2011,
August). West Evans Avenue Bridge Condition Inspection Report Addendum
1 Additional Fatigue Tesing and Evaluation. Unpublished.
Frangopol, D. & Curley, J. (1987, July ). Effects of Damage and Redundancy on
Structural Reliability. Journal of Structural Engineering 113(7), 1533-1549.
Frost, N. E., Marsh, K. J. & Pook, L. P. (1974). Metal Fatigue. Oxford, England:
Clarendon Press.
Ghahremani, K. &Walbridge, S. (2011). Fatigue Testing and Analysis of Peened
Flighway Bridge Under In-Service Variable Amplitude Loading Conditions.
International Journal of Fatigue 33, 300-312.
Hawkins, K. P. City and County of Denver. (1996, August 8). Column Analysis -
West Evans Avenue over Santa Fe Drive. Unpublished.
Howell, D. & Shenton, H. (2006). System for In-Service Strain Monitoring of
Ordinary Bridges. Journal of Bridge Engineering 11(6), 673-680.
Kwon, K. & Frangopol, D. (2010). Bridge Fatigue Reliability Assessment Using
Probability Density Functions of Equivalent Stress Range Based on Field
Monitoring Data. International Journal of Fatigue 32, 1221-1232.
Li, C. City and County of Denver. (2000, May ). West Evans Avenue Bridge Over
South Santa Fe Drive Bearing Field Inspection Report. Unpublished.
Li, C. City and County of Denver. (2001, September). West Avenue Bridge Over
South Santa Fe Drive Movement and Stress Study Report. Unpublished.
LONCO, City and County of Denver. (1994, December 2). 1994 Inspection of
Structure No. D-03-V-180. Unpublished.
LONCO, City and County of Denver. (1996, October 10). 1996 Inspection of
Structure No. D-03-V-180. Unpublished.
LONCO, City and County of Denver. (1997, October 22). 1997 Inspection of
Structure No. D-03-V-108. Unpublished.
LONCO, City and County of Denver. (1998, December 29). 1998 Inspection of
Structure No. D-03-V-108. Unpublished.
89


LONCO, City and County of Denver. (2000, September 15). 2000 Inspection of
Structure No. D-03-V-108. Unpublished.
LONCO, City and County of Denver. (2002, October 3). 2002 Inspection of
Structure No. D-03-V-108. Unpublished.
LONCO, City and County of Denver. (2004, August 30). 2004 Inspection of
Structure No. D-03-V-108. Unpublished.
LONCO, City and County of Denver. (2006, October 16). 2006 Inspection of
Structure No. D-03-V-108. Unpublished.
Pook, L. (1983). The Role of Crack Growth in Metal Fatigue. Bristol, England:
J.W. Arrowsmith Ltd.
Pook, L. (2007). Metal Fatigue: What It It, Why It Matters. Dordrecht,
Netherlands: Springer.
Poutiainen, I. & Marquis, G. (2006). A Fatigue Assessment Method Based on
Weld Stress. International Journal of Fatigue 28, 1037-046.
Rens, K. L. & Transue, D. J. (2002, July/August). Tomographic Imaging of
Cracked Pier Cap of Evans over Santa Fe Bridge. Concrete Repair
Bulletinl 2-15.
Schijve, J. (2009). Fatigue of Structures and Materials. (2nd ed.), Dordrecht,
Netherlands: Springer Science+Business Media.
Short Elliott Hendrickson Inc., City and County of Denver. (2008, October 23).
2008 Bridge Inspection Report of Structure No. D-03-V-108. Unpublished.
Short Elliott Hendrickson Inc., City and County of Denver. (2010, November 4).
2010 Bridge Inspection Report of Structure No. D-03-V-108. Unpublished.
Spangenburg, L. (1876). The Fatigue of Metals Under Repeated Strains. New
York: Van Nostrand.
Stefanescu, D. M. (2011). Handbook of Force Transducers Principles and
Componenets. Springer-Verlag Berlin Heidelberg.
Zhao, Z. & Haidar, A. (1994, May ). Fatigue-Reliability Evaluation of Steel
Bridges. Journal of Structural Engineering 120(5), 1608-1623.
90


Full Text
Bridge Design Specifications, AASHTO issued The Guide Specifications for
Fatigue Evaluation of Existing Steel Bridges based on research by NCHRP
(Bowman et al., 2012). NCHRP developed these procedures because the
AASHTO fatigue design was not suited for existing bridges. AASHTO linked the
guide back to their LRFD Bridge Design Specifications when information about
the existing bridge was insufficient, such as truck loading or average daily truck
traffic; it was required to use the design values. Current issues of the AASHTO
codes still reference one another when insufficient information is provided about
the existing bridge and traffic conditions. In 2003, the AASHTO Manual for
Condition Evaluation and LRFR of Highway Bridges (LRFR Manual) was
published in lieu of a new addition or update to the 1990 Guide Specification for
Fatigue Evaluation of Existing Steel Bridges. The LRFR manual encompassed
evaluation for multiple bridge types, bridge conditions, and contained the fatigue
evaluation of steel bridges as a section instead of the entire manual (Bowman et
al., 2012).
A new element was introduced in the fatigue life calculations, the resistance
factor, Rr. For design purposes the design fatigue life would be synonymous
with the minimum fatigue life, Rr=1.0 and would not create any changes to the
design calculations. The resistance factor has two other categories, besides the
minimum fatigue life, including the evaluation life and the mean fatigue life, where
Rr varies for each depending on the detail category being evaluated. These
three resistance factors equate the mean fatigue life to a 50% probability of
failure, evaluation life at 16% probability of failure (one standard deviation away
9



PAGE 1

FATIGUE ANALYSIS OF EVANS AVENUE BRIDGE OVER SANTA FE DRIVE by Elisabeth Jaclyn Cole B.S ., University of Colorado Boulder, 1996 A thesis submitted to the Faculty of the Graduate School of the University of Colorado Denver in partial fulfillment of the requirements for the degree of Masters of Science Civil Engineering 2012

PAGE 2

! ii This thesis for the Masters of Science degree by Elisabeth Jaclyn Cole has been approved for the Civil Engineering Program Dr. Kevin L. Rens, Chair/Advisor Dr. Yail Kim Dr. Rui Liu November 28 2012

PAGE 3

! iii Cole, Elisabeth (M.S., Civil Engineering) Fatigue Analysis of Evans Avenue Bridge Over Santa Fe Drive Thesis directed by Professor Dr. Kevin L. Rens ABSTRACT The West Evans Avenue Bridge over South Santa Fe Drive was built in 1972. In 2009, an inspection was completed to assess the current condition of the bridge for recommendations on an upcoming rehabilitation project. Initial results through use of visual inspection and analysis for compliance with the AASHTO Manual for Bridge Evaluation and the AASHTO LRFD Bridge Design Specifications determined retrofits to the steel girders containing the partial length cover plates would be necessary to extend the fatigue life of the bridge for another 20 plus years costing the City and County of Denver a n additional one million dollars. Due to the age of the bridge the most conservative estimates were used in the calculations for determining the remaining fatigue life of the steel girders. This prompted field testing to measure the actual stress ranges on the bridge. 20 strain gauges were placed on the bottom flanges of the steel girders of concern from March 8, 2011, through April 11, 2011. The remaining fatigue life of the bridge was calculated at 53 years requiring no retrofits to the existing stee l girders at this time. This thesis presents the analysis of the AASHTO calculations requiring retrofits for the steel girders, the procedure and results of

PAGE 4

! iv the strain gauge testing resulting in no retrofits, and a cost savings for the City and County of Denver by completing both fatigue analysis. The form and content of this abstract are approved I recommend its publication. Approved: Kevin L. Rens

PAGE 5

! v TABLE OF CONTENTS Tables ......................... ................................................................................ix Figures ..................................................................................................... xi Chapter 1. Introduction ........................................................ .......... ...........................1 2. Literature Review of Fatigue .......................... ........ .......... .......................4 2.1 Brief Metal Fatigue History............ ........................ .......... ......................4 2.2 Fatigue Threshold and Crack Initiation ...................... .......... .................5 2.3 AASHTO Fatigue Design and Evaluation......................... .......... ..........6 2.4 Field Strain Measurements................................ .......... .......................1 1 3. History of the Evans Bridge ........................................ ......... .................13 3.1 Construction History ................................ ............. .......... .....................13 3.2 Repair History ..................................................... .......... ......................15 3.3 Inspection History ................................................. .......... .................... 18 3.3.1 Biannual Inspections ........... .............................. .......... ................... ...18 3.3.2 Additional Inspections and Analysis ...... ........... .......... .............. .........21 3.3.2.1 1996 Column Capacity Analysis ..... ................. .......... ............ ........22 3.3.2.2 2000 Bearing Field Inspection ....... ........................ ......... .............. .23 3.3.2.3 2001 Movement and Stress Study Report .... ............ .......... ..... ......26 3.3.2.4 2009 Condition Ins pection ..... .............................. ......... ............... ..29

PAGE 6

! vi 4. Rehabilitation Project ...... ....................................... .......... ................... ..30 4.1 Project Initiation ... ......................................... ......... ..... ..................... ....30 4.2 Visual Inspection ... ........................................ .......... ........................ .....30 5. Visual Inspection and Fatigue Life Design ........... .......... .................. ....32 5.1 Traffic Counts ... .................................................. .......... .................... ...32 5.2 Bridge Girder Modeling .... ..................................... .......... .................. ..32 5.3 Fatigue Analysis .... ............................................ .. .......... ...................... 33 5.3.1 Stress Range ..... ................................................. .......... ................... .33 5.3.2 Nominal Fatigue Resistance .... .................. .......... .......................... ..34 5.3.2.1 Fatigue L ive Load Factor ....... .................. .......... .......................... .34 5.3.2.2 Live Load Distribution Factor .... .................... .......... ...................... 35 5.3.2.2.1 Moment Distribution on Exterior Girders ..... ..... .......... ............... .35 5.3.2.2.2 Moment Distribution on Interior Girders ... .................. .......... ... ...37 5.3.3 Infinite Fatigue Life ... ...................................................... .......... ....... .38 5.3.4 Finite Fatigue Life .............. ............................. ......... .................... ...42 6. Strain Transducer Testing Procedures ... .............. ......... ..................... .46 6.1 Strain Transducer History ................................. .......... .................... ...46 6 .2 Strain Transducer Development ... ................. .......... .......................... .46 6.3 Strain Transducer Installation .. ....................... .......... ........................ ..47 6.4 Transducer Removal ... .............................. .......... ............................... .53 7. Strain Transducer Data Collection and Analysis ... .... .......... ................. .54 7.1 Traffic Counts .. ............................................................... .......... ........ ...54

PAGE 7

! vii 7.1.1 Traffic D ata .. ................................................................. ......... ....... ....5 4 7.1.2 Average Daily Truck Traffic .. .......................... .......... ...................... ..55 7.2 Control Test ... ............................................ .... ......... .......................... ..55 7.2.1 Control Test .. .......................................... ......... .............................. ..55 7.2.2 Control Test Results .. ........................... ......... ............................... ...58 7.3 Stress Cycles .... ......................................... .......... .............................. .64 7.3.1 Stress Cycle Counts ... ................................ ......... .......................... ..64 7.3.2 Stress Cycle Data Analysis for 80' Girder Sp an .. .... ......... ............. ..67 7.3.3 Stress Cycle Data Analysis for 95' Girder Span ... ........ ......... ......... .76 8. Results .... ........................................................................... .......... ......... 79 8.1 Visual Inspection Fatigue Life Design Results .. .......... .......... ............ ..79 8.2 Strain Transducer Fatigue Life Results ..... .................. .......... .............. 80 9. Cost Comparison .... .................................................... .......... ................ 83 10. Conclusions and Future Research ... ............... .......... ......................... .84 10.1 Conclusions......................................................... ..............................84 10.2 Future Research.................. ................................ ..............................85 References .............................................................................................. .. 88 Appendix A. Section Properties of 80' Span............................... ..............................92 B. Section Properties of 95'Span................................. ..............................94 C. 80' Span Visual Inspection Calculations .................... .......... ......... ..... .. .96 D 95' Span Visual Inspection Ca lculations .. .................. .......... ........... ... 100

PAGE 8

! viii E. ADTT Counts.......................................................... .............................104 F 80' Span Strain Gauge Analysis............................. .............................1 09 G 95' Span Adjusted Calculations.. ........................... .................... ...... ..119

PAGE 9

! ix LIST OF TABLES Table 5 .1 80' Span Girder Stress Distribution...... .................. .......... ...................4 1 5 .2 80' Span Girder Bottom Flange Fatigue Life Check........ ......... ..........42 5 3 80' Span Girder Bottom Flange Fatigue Life ..... ............. .......... ...........45 5 .4 95' Span Girder Bottom Flange Fatigue Life .................. .......... ........... 45 7.1 Control Test Results Summary................................... ............... ..........63 7 .2 Stress Cycle Count Summary.. ................... .................. .......... ............65 7.3 Estimated Minimum Finite Life of 80' Span Girders with Minimum Stress Range of 1.0 to 1.5 ksi ................. ... .......... ..............71 7.4 Estimated Minimum Finite Life of 80' Span Girders with Minimum Stress Range of 2.0 to 2.5 ksi............ ...... .......... .............. ...73 7.5 Estimated Evaluation Finite Life of 80' Span Girders with Minimum Stress Range of 2.0 to 2.5 ksi............. ......... .......... .... ......... 7 5 7.6 Estimated Mean Finite Life of 80' Span Girders with Minimum Stress Range of 2.0 to 2.5 ksi .......... ..... ..... .......... .. ..... ........75 7.7 Calculated Fatigue Life for the 95' Span Girders......... .......... ..............78

PAGE 10

! x 8.1 Estimated Remaining Des ign Fatigue Life for 80' Span ......... .......... .. .80 8.2 Estimated Remaining Design Fatigue Life for 95' Span. .... .......... ......80 8.3 Estimated Remaining Evaluation Fatigue Life for 80' Span .... .......... ..81 8.4 Estimated Remaining Evaluation Fatigue Life for 95' Span ... .......... .. ..82

PAGE 11

! xi LIST OF FIGURES Figure 2.1 S N Curve for AASHTO Detail Categories.....................................................8 3.1 Evans Bridge Plan and Elevation 1966..... .......... ................................ 1 4 3.2 Rusted Steel Girder Below Santa Fe Ramp Abutment........... .......... ..17 3. 3 Flashing Below Abutment and New Paint on Steel Girder.... .......... ....18 3.4 Evans Bridge Elevation 1996............ ................................ .......... ........ 22 3.5 Pier 6 Expansion Bearing.... ........................ ...................... ......... ........25 3.6 Deteriorated Concrete Pier Cap ................. ....................... .......... ........2 8 5.1 Evans Bridge 2009 ADTT Counts ....................................... .......... .... ...32 5 2 Evans Bridge Cross Section.............. ...... ........................ .......... .........37 6.1 BDI ST350 Strain Transducer.......... ..... .......................... .......... ... ........47 6.2 Strain Transducer Locations........ ....... ........................... .......... ........... .48 6 .3 Transducer Location to Partial Cover Plate.... .... .......... .......... ....... ......49 6.4 Aluminum Cover Around Transducer. ............................ .......... .......... ..50 6 5 14 of 20 Installed Transducers ..................................... .......... ............ ..51 6.6 Structural Monitoring System ....................................... .......... .......... ....5 2 6.7 Structural Monitoring System Power Source. .................... .......... ... .....52 7 1 Truck at Base of Evans Bridge for Control Test.. ........... .......... ....... ....56 7.2 Truck Climbing Ramp of Evans Bridge for Control Test. .... .......... ... ...56

PAGE 12

! xii 7.3 Truck Approaching Strain Transducers During Control Test.. .............. ................................... .......... ..............57 7.4 Truck Completing Control Test.. ............................. .......... .................. 57 7.5 Control Test 1 Results for Transducers F1 K1. ........ ......... ......... ....... .59 7.6 Control Test 2 Results for Transducers F1 K1 ........... ......... ............. ..60 7.7 Control Test 3 Results for Transducers F1 K1 ...... .. ......... ................ .61 7.8 Control Test 4 Results for Transducers F1 K1 ...... .......... ................... 62 7.9 Strain Transducer Locations........................... ..... ... .......... ................. .67

PAGE 13

! 1 1 Introduction Fatigue failure was a phenomenon that started gaining attention in the mid 19 th century and by the beginning of the 20 th century researchers had uncovered the causes of fatigue The researchers began identifying fatigue thresholds for various materials although f atigue thresholds were not easily quantifiable because of the scatter in the data. This was not due to lack of research as it was determined that fatigue is largely based on impurities of the member and each member can contain different amounts of impurities increasing or decreasing the fatigue lives of members fabricated from the same materials. Throughout the 20 th century, researchers and engineers continued evaluating the causes and effects of fatigu e in steel members of different sizes and shapes and began creating bridge design requirements Although much progress was made within a short amount of time, b ridge failures were increasing in the mid 20 th century. In 1978 d ue to the increase in bridge failures the Federal Highway Administration began mandating that all bridges longer than 20' would require biannual inspections ( F ederal Highway Administration, n.d. ) The biannual inspections aided in the engineer's aw areness of the bridge condition; h owever, evaluati ng a bridge for fatigue failure was still nonexistent. Utilizing fatigue design for the assessment of an existing bridge was proving to be overly conservative resulting in requiring expensive repairs to the structures. Methods for evalua ting existing bridges for fatigue beg an to emerge in the late 1980's By 1990 an evaluation guide of existing steel bridges was created

PAGE 14

! 2 providing an assessment of existing bridges. This was f ollowed by development of better evaluation techniques by the turn of the 21 st century. Current evaluation methods provide the most accurate results of bridge fatigue analysis for measurements taken in the field, including actual traffic data and strain measurements gathered at fatigue critical details. Closer evaluation of these methods will be looked at in a current project located in Denver, Colorado. The West Evans Avenue Bridge spanning over Santa Fe Drive was built in 1972 and has been part of the City and County of Denver's biannual inspecti ons since th e 1980's. During the life of the bridge both small and large scale repairs have been undertaken in an effort to maintain the bridge's ability to publicly operate. In 2009 the Evans Bridge was thoroughly inspected for an upcoming rehabilitation projec t. T he City and County of Denver was designing the rehabilitation to last for the next 20 years and s ince fatigue in existing bridges has been a problem, especially for older bridges, a fatigue analysis was conducted on the steel girders of the Evans Bridge. The analysis was based on visual inspection which required mostly fatigue design values to be u sed thus creating a conservative estimate that the fatigue life of the bridge would not meet the 20 year requirement. Repairs and retrofits to the existing ste el girders would make the girders surpass the 20 year minimum, but would be very costly. Advances in the collection of strain measurements provided opportunity for the bridge to be tested for a minimal cost. Data was collected at the fatigue prone locati ons and the fatigue life was reanalyzed. This thesis analyze s the fatigue life of the steel

PAGE 15

! 3 girders using both the visual inspection method and the data collected in the field This includes comparing the results and costs associated with each method's so lution

PAGE 16

! 4 2 Literature Review 2 .1 Brief Metal Fatigue History Documented research on metal fatigue began in the 1830's following multiple unexpected mechanical failures occurring after extended use (Frost et al 1974). These failures were caused in devices where low stresses were applied multiple times. August Wšhler an early researcher of metal fatigue ( Schijve, 2009 ), was quoted with referring to fatigue as rupture of material may be caused by repeated vibr ations, none of which att ain the absolute breaking limit ( Spangenburg, 1876). The idea Wšhler presented was that materials under repeated loadings could fail even if that load is below the fracture limit. Wšhler also determined that there is a stress range in which a material did not fracture no matter the number of times the element was loaded ( Frost et al 1974 ). This has become to be known as the fatigue limit or threshold, in which each member has a stress limit where cyclic loads applied below t he threshold will give infinite life, and cyclic loads applied above the threshold but below the fracture limit will pr ovide a finite life span. Finite fatigue life is calculated by the number of loadings a member can withstand before complete failure ( Sc hijve, 2009; Pook, 2007 ). Wšhler was not the only researcher to come to this conclusion in the 19 th century. William Rankine discovered during the 19 th century that the metal under this repeated loading had a brittle app earance ( Frost et al 1974 ). Thi s discovery le d to the idea that the metal would slowly deteriorate, becoming

PAGE 17

! 5 crystalline and brittle in nature, which would ultimately produce a complete failure. In the early 20 th century Ewing and Humphrey further researched the changing of the metallic properties on the surface of the element during the process of the repeated loadings ( Pook, 1983 ; Pook, 2007 ). Researchers have also determined that developments in the metals dur ing the fatigue tests can be categorized into three pha ses ; the crack initiation phase, crack growth phase and failure of the member ( Zhou and Haldar, 2006 ; Schijve, 2009 ). 2.2 Fatigue Threshold and Crack Initiation The crack initiation p hase creates micro fractures in the surface of the element in as little as one load cycle provided the applied load is above the fatigue threshold ( Schijve, 2009 ). Micro fractures develop in the surface due to stress concentrations at surface irregularities ( Frost e t al 1974 ). Surface irregularities can be attributed to various life stages including manufacturing, surface preparation, and even environmental factors such as corrosion This variety of surface irregularities that each member has creates different le ngths of fatigue life making it difficult to quantify exactly the length of fatigue life for each type of material ( Frost et al 1974; Schijve, 2009 ). Not all m icro fractures develop into visible cracks those that do take a long time to turn into visib le cracks, making the majority of the fatigue life in the crack initiation phase ( Schijve, 2009 ). This principle can redefine the fatigue threshold to "the largest stress amplitude which does not lead to continuous crack growth until failure" ( Schijve, 2009 pg. 31).

PAGE 18

! 6 Numerous experiments have been conducted to determine if increasing the member's size would increase the fatigue threshold. Bending fatigue tests have proven that increasing the member's size actually decreases the fatigue threshold ( Frost et al 1974; Schijve, 2009 ). As previously stated the micro fractures occur at surface imperfections containing a higher stress concentration. With an increased member size "the probability of having such weak spots is larger for a larger material surf ace area carrying the maximum stress cycle" ( Schijve, 2009 pg. 153). Welded locations have a higher probability of crack propagation at the toe of the weld largely due to two occurrences. Firstly, the weld can contain a large number of defects S econdl y, because of the welding process the contraction of the weld when it cools creates re sidual stress within the weld ( Poutiainen and Marquis, 2005; Schijve, 2009; Pook, 2007 ). Fillet welds contain even higher concentrations of stress than other types of w elds, because the welds do not penetrate through the entire member ( Frost et al 1974 ). Peening welds is a method of reducing the number of imperfections with in the weld, as well as loading the weld with residual compression. Current r esearch on peened highway bridge welds has proven to benefit the fatigue life of a large range of probable bridge loading conditions ( Ghahremani and Walbridge, 2010). 2.3 AASHTO Fatigue Design and Evaluation As bridge failures became an increasing issue i n the United States, culminating with the 1967 collapse of the Silver Bridge due to fatigue failure of an

PAGE 19

! 7 eyebar supporting the main span (Connor et al 2005 ), the Federal Highway Administration began implementing policies for bridge inspections. The Ame rican Association of State Highway and Tr ansportation Officials (AASHTO) published their 10 th E dition of the AASHTO Standard Specifications for Highway Bridges in 1969. This edition was the second appearance of fatigue design provisions, the first published in 1965. However, the 10 th E dition determined an allowable fatigue stress from such factors as the applied load, highway classification, steel strength, detail type, and ratio of minimum to maximum stress ( Bowman et al 2012 ). The 12 th Editio n of the AASHTO Standard Specifications for Highway Bridges, published in 1977, addressed common details in steel bridges that were considered fatigue sensitive ( Bowman et al 2012 ). This list of details, currently known as the detail categories, ranged from A through F, although some changes have occurred and the list no longer includes F the detail categories for the most part are the same ( Frost et al 1974; Bowman et al., 2012 ). In addition to the detail categories the 12 th Edition also included a stress range. As identified by studies and research, the stress range was determined to be a function of the detail category and number of applied cycles, not the strength of the material ( Bowman et al 2012 ). AASHTO employed the S N curve method for determining fatigue life, which uses the stress range and number of cycles applied. To determine a fatigue threshold, as well as the number of cycles at different stresses the detail was able to withstand, each detail category wa s thoroughly tested by National

PAGE 20

! 8 Cooperative Highway Research Program (NCHRP) ( Zhao and Haldar, 1994 ). The fatigue thresholds used by AASHTO for the detail categories were calculated two standard deviations away from the mean producing a 2% to 2.5% probabi lity of failure for each detail category (Bowman et al., 2012). AASHTO's detail categories S N curve for a two standard deviation step in the fatigue threshold is shown below in Figure 2. 1 Figure 2. 1 S N Curve for AASHTO Detail Categories Until 1994, when AASHTO introduced the LRFD Bridge Design Specifications, no significant changes were made to the fatigue design methods ( Bowman et al 2012 ) The major revision to the fatigue design of the LRFD Bridge Design Specification from the Standard Specific ations for Highway Bridge Design was in the applied load. In 1990, prior to the introduction of the LRFD !" #!" $!" %!" &!" '!" (!" )!" #*!!+,!'" #*!!+,!(" #*!!+,!)" #*!!+,!-" !"#$%%&'()*$+&,%-& ./01$#&23&4567$%& 88!9:;&<(=*/$&4/#>$%& ." /" /0" 1"2"10" 3" +" +0" .45" /45" /045"2"1045" 145" 345" +45" +045"

PAGE 21

! 9 Bridge Design Specifications, AASHTO issued The Guide Specifications for Fatigue Evaluation of Existing Steel Bridges based on research by NCHRP ( Bowm an et al 2012 ). NCHRP developed these procedures because the AASHTO fatigue design was not suited for existing bridges. AASHTO linked the guide back to their LRFD Bridge Design Specifications when information about the existing bridge was insufficient, such as truck loading or average daily truck traffic; it was required to use the design values. Current issues of the AASHTO codes still reference one another when insufficient information is provided about the existing bridge and traffic conditions. In 2003, the AASHTO Manual for Condition Evaluation and LRFR of Highway Bridges (LRFR Manual) was published in lieu of a new addition or update to the 1990 Guide Specification for Fatigue Evaluation of Existing Steel Bridges. The LRFR manual encompassed eva luation for multiple bridge types bridge conditions and contained the fatigue evaluation of steel bridges as a section instead of the entire manual ( Bowman et al 2012 ). A new element was introduced in the fatigue life calculations, the resistance fac tor, R R For design purposes the design fatigue life would be synonymous with the minimum fatigue life, R R =1.0 and would not create any changes to the design calculations. The resistance factor has two other categories, besides the minimum fatigue life, including the evaluation life and the mean fatigue life, where R R varies for each depending on the detail category being evaluated. These three resistance factors equate the mean fatigue life to a 50% probability of failure, evaluation life at 16% probability of failure ( one standard deviation away

PAGE 22

! 10 from the mean), and the minimum fatigue life as 2% probability of failure ( two standard deviations from the mean) ( Bowman et al 2012; AASHTO, 2011 ). As r econstruction and retrofits to bridges can be costly, the resistance factor provides a valuable tool for the evaluation process. Provided no cracks are visible at the fracture critical detail, AASHTO requires retrofits to all cracked members, the resistance factor used is determined by the engine er's judgment. Although it is possible to achieve negative remaining fatigue life, which means that the detail has surpassed the resistance factor's probability of failure ( Bowman et al 2012 ) i t is quite common for a bridge to achieve a greater fatigue life than that provided by minimum design, or 2% probability of failure A steel detail can still surpass the mean resistance factor, as it is a 50% probability of failure, meaning 50% of the tests conducted have surpassed that value. This is why when e valuating an existing bridge it is up to the engineer to decide which resistance factor is used in determining remaining fatigue life. Following the improvements to the LRFR Manual, AASHTO published the Manual for Bridge Evaluation (MBE) in 2008 and issued a 2 nd Edition in 2011. The MBE address ed the use of collected field strain data used in lieu of the calculated stress range which is more accurate, requires less factors of safety, and ultimately produces longer fatigue life with more accuracy than the design method ( Bowman et al 2012; AASHTO 2011 ).

PAGE 23

! 11 2 .4 Field Strain Measurements Field strain measurements have been increasing in popularity in order to avoid costly retrofits to existing bridges (Zhou, 2006). Developments in the strain ga uge monitoring systems have created portable systems that can collect live data using web based applications ( Howell and Shenton, 2006). One consideration for field measurements is the inclusion of all the stress cycles collected even those below fatigue threshold. For lower fatigue categories D, E, and E', the percentage of cycles below the fatigue threshold account for the majority o f the vehicle traffic (Zhou, 2006). Including all of the gathered stress cycles lowers the ca lculat ed stress range, ultimately providing an overestimation of fatigue life Some probabilistic methods have been evaluated to determine the cut off of the stress range ( Kwon and Frangopol, 2010) while other cut off methods include using all stresses a bove 50% of the constant amplitude fatigue limit (Zhou, 2006), and still others truncate the stress range at the constant amplitude fatigue thres hold ( Alampalli and Lund 2006). The ultimate decision relies upon engineering judgment as to where to remove the lower stress cycles in an effort to produce an acceptable stress range. Using a strain gauge monitoring system the New York State Patroon Island Bridge was evaluated to have a minimum safe fatigue life of 27 years at a detail category E location (Alampalli and Lund, 2006). The Cleveland Central Viaduct was found to have insufficient remaining fatigue life using the AASHTO visual inspection evaluation method, but field testing proved the bridge to have infinite fatigue based on the most fatigue pr one detail location (Zhou, 2006) As

PAGE 24

! 12 concluded by Kwon and Frangopol, "The field monitoring data can be successfully used for fatigue reliability assessment and fatigue life prediction of existing steel bridges" ( 2010, pg. 1232).

PAGE 25

! 13 3. History of the Evans Bridge 3.1 Construction History Drawings for the Evans Bridge over Santa Fe Drive in Denver, Colorado, date back to 1966; there is no recorded documentation prior to this. Only one page of the 1966 drawings was archived which consists of plan and elevation view s of the bridge and a note stating that these dra wings are for reference only and not part of the construction plans Although this drawing was not part of the construction set, it has the girder sizes and spans that we re used in the final construction of the bridge as shown in Figure 3.1

PAGE 26

! 14 Figure 3.1 Evans Bridge Plan and Elevation 1966 (City and County of Denver West Evans Avenue and South Santa Fe Drive Grade Separation Plan & Profile, Project Number 9204, 1966) The City and County of Denver Public Works Division (CCD) submitted final drawings for approval and construction in August 1971 These drawings included the structure, retaining walls, abutments, deck, bearing and expansion devices, approach details, railway signals, railroad grading, painting, lighting, and guardrail layouts. Construction of the bridge began in 1972 and was comple ted later that year. The bridge was constructed with a composite concrete deck, and consists of 12 hot rolled steel I beams over 9 spans with an overall length of 765 feet.

PAGE 27

! 15 In 1983, the Colorado Department of Transportation (CDOT) made plans to construct ramps connecting Santa Fe Drive with Evans Avenue. However, in order for this construction to progress CDOT needed to gain approval from CCD to connect these ramps to the existing Evans Brid ge. CCD agreed to this construct ion and designed modifications to the bridge to allow ramp access. This required removal of the barrier walls and construction of new turn lanes and traffic signals. CDOT and CCD worked together to design the ramps to fit the current bridge. However, th e bridge and the ramps remain two separate entities; CCD maintains the bridge, while CDOT maintains the ramps. 3.2 Repair History Although a few repairs were made in 1983 with the addition of CDOT's ramps, there were many more to be done to keep the bridge in good working or der. 1985 brought on the first major round of repairs to the bridge. The repairs included completely resurfacing the road, replacing the sidewalks, railings, and concrete barriers, placing new backfill around the structure, and up dating the landscape. The next round of bridge repairs came in 1995, following a field inspection in 1994. Refer to section 3.3 for more information regarding the 1994 inspection. Repairs made to the Evans Bridge at this t ime were the

PAGE 28

! 16 expansion joints, the fixed and expansion bearing s abutments and new asphalt resurfacing. These repairs continued through 1997. In 2010, the steel girders below the abutments of the Santa Fe Drive ramps were severely rusted and required attention, refer to Figure 3.2. The high levels of rust were due to a deteriorating abutment condition causing water to leak through. Although CDOT owns and operates the ramps connecting Santa Fe Drive and Evans Avenue, they did not want pay for half of a new abutment joint at these loc ations. This required that CCD install flashing to avoid water damage to the steel girders below since they were unable to install a new abutment With flashing installed to divert leaks from affecting the steel girders, the girders were then grinded do wn to remove the rust and then repainted, refer to Figure 3.3.

PAGE 29

! 17 Figure 3. 2 Rusted Steel Girder Below Santa Fe Ramp Abutment

PAGE 30

! 18 Figure 3. 3 Flashing Below Abutment and New Paint on Steel Girder 3.3 Inspection History 3.3.1 Bi a nnual Inspections In 1980 the Federal Highway Administration implemented a policy that requires all bridges with spans twenty feet or longer to be inspected on a biannual basis. D ue to this Federal policy, CCD started a bridge inspection program for the 538 bridges within the limi ts of CCD's jurisdiction All of CCD's bridges are inspected either biannually or tri annually based on the bridge's length. Bridges with twenty foot spans or

PAGE 31

! 19 longer are inspected every other year which account for 207 of CCD's bridges. The 331 CCD b ri dges with spans less than twenty feet are inspected every third year. Inspections of smaller bridges are not required by the Federal Highway Administration, but have been completed by CCD to maintain records of all the bridges in Denver. Records of the Evans Bridge inspections are available at the City and County of Denver Public Works Division office for every two years starting in 1994 Inspection reports prior to 1994 have been archived and have proved difficult to retrieve The 1994 inspection re ported p oor asphalt conditions, moderate damage to the expansion joints, light rusting through the steel girder paint, poor bearings, severe spalling of the concrete caps, and moderate delamination of the concrete columns. The condition of expansion joint s were poor and needed urgent repairs (LONCO, 1994) This inspection report prompted the repairs made in 1995 Asphalt conditions of the 1994 inspection had worsened by the 1996 inspection, extending a continua tion of repairs into 1997. Required repairs from this inspection were the expansion joints at the abutments due to leaking. Other concerns were the cracking concrete at the railing connections cracking on the bottom of the concrete deck, joint separation of the wingwall and deterioration of the c oncrete curbs and sidewalks (LONCO, 1996)

PAGE 32

! 20 Following the repairs in 1997, a final inspection was completed and resulted in no urgent repairs. Maintaining the two year inspectio n cycle, 1998 al so warranted no urgent repairs. The majority of the comments in the 1998 inspection report stated that the repair had been made in 1997, however, there were still a few programmed repairs and general maintenance items, such as clean ing deck drains, patch i ng potholes, and remov ing sand and gravel from the sidewalks (LONCO, 1998) Inspections complete d in 2000, 2002, 2004, and 2006, resulted in no urgent repairs. However, programmed repairs and safety improvements increased exponentially over the four inspections (LONCO, 2000; LONCO, 2002; LONCO, 2004; LONCO, 2006) The 2000 inspection report listed cleaning deck drains, patching potholes, and installing safety markers as the improvements and future repairs, amounting to $1,400. This is in contrast to the 2006 report which listed patching potholes at multiple locations, cleaning drains, replacing rubber fillers at ramp connections, painting girders, rehabilitating delaminated concrete cap, installing safety reflectors, replace missing posts, and instal ling a cover over the J box. The 2006 programmed repairs and safety improvements would cost $32,300 to complete. T he inspection completed in 2008 used a new reporting system employed by CCD Each item needing attention had a priority desi gnation

PAGE 33

! 21 assigned. No urgent repairs were listed in this report. Installing safety markers and replacing missing rails were noted as safety concerns. Replacing expansion joints, and cleaning and painting the bearings were listed as programmed repairs. Maintenan ce issues were cleaning the deck drains, patching potholes and spalls, and painting the railing. The estimated cost of these repairs came to $31,800, which was in alignment to the approximate cost s estimated in 2006, inc luding the future repair cost (Shor t Elliott Hendrickson Inc. 2008) The 2010, the biannual inspection report read similar ly to the 2008 inspection ; however, a major difference in the 2010 inspection report was an increase in quantity of the repairs with an estimated cost of $40,560. The additional cost of approximately $8,000 implies that the bridge had further degraded since 2008 which is evid ent by a 60% increase in the number of potholes (Short Elliott Hendrickson Inc. 2010). 3.3.2 Additional Inspections and Analysis In addition to the biannual inspections, CCD has historically contracted with private companies to complete additional inspect ions on the Evans Bridge. The additional inspections are requested by CCD for reasons deemed necessary for the assurance of the bridge safety. Typically, the

PAGE 34

! 22 additional inspections are completed due to questionable quality of major structural elements that could require large scale, expensive repairs. 3.3.2.1 1996 Column Capacity Analysis The first additional inspection in this series was compl eted in 1996, by URS Consultants Inc., for the capacity analysis of a deteriorated column located to the south side of bent #6, refer to Figure 3.4 below The bents sit atop a Teflon bearing material which ideally create s a frictionless connection to prevent the transfer of shear and moment to the concrete columns. Spalling concrete, rusted bearing pads, and missing Teflon on top of the bearing pad caused concern that the connection was no longer frictionless and causing the break down of the column, prompting an in depth analysis of the column. Figure 3. 4 Evans Bridge Elevation 1996 ( City and County of Denver West Evans Avenue Viaduct Resurfacing and Expansion Joint Replacement Project, Project Number 95 294A, 1996)

PAGE 35

! 23 The west side of Bent #6 is at an existing expansion joint. Thermal expansion of the bridge will engage the bent forcing it to move. Ideally, Bent #6 will slide frictionless atop a bearing which will not transfer shear or moment into the concrete column under the bearing. URS analyzed this ideal condition and confirmed that no shear or moment would be transferred into the column below (Hawkins, 1996) Based on information provided from CCD about the current condition of the spalling column and rusted b earing pad, URS completed a second analysis of the column under the poor conditions. URS assumed the connection was fixed, and reported that the analysis showed both moment and shear transferred from the bent into the column. However, the amount of shear and moment transferred was still within the acceptable factor of safety limits. URS also reported that assuming a fixed condition was conservative, since it was unlikely that the bent would not slide given enough force. The final determination to the ca use of the spalling concrete column and rusted bearing was from the leaking expansion joint above the west side of Bent #6. 3.3.2.2 2000 Bearing Field Inspection During CCD's programmed 2000 inspection, observ ations that the expansion bearings on Pier 6 and the east abutment were not sliding

PAGE 36

! 24 caused concern. Further apprehension was caused by the rust pack and deformation present between the stainless steel plates, sole plates, and Teflon pads of the expansion bearing s. These concerns required CCD to hire a c onsultant to complete a more detailed inspection. UR S Greiner Woodward Clyde (URS ), the same company who analyzed the column capacity in 1996, was consulted again to conduct a bearing field inspection. This inspec tion was to complete a movement study of Pier 6 while also determin ing the column profile and conduct ing a bearing inspection for both Pier 6 and the east abutment (Li, 2000) The objectives of the inspection were to record the bearing condition, measure the bearings physical dimensions, observe the expansion bearings performance, and make rehabilitation recommendations. URS confirmed CCD's inspection results that the expansion bearings at Pier 6 and the east abutment were no longer sliding. The determine d causes of this were due to the rust pack around the bearing area, as well as deformation of the plates and Teflon preventing the bearing from slid ing as shown in Figure 3.5 The expansion joint above Pier 6 appeared to be leaking which was a probable c ause for the rust pack of the expansion bearing. Replacement of both bearings was recommended since they were no longer functioning as required per the original design.

PAGE 37

! 25 Figure 3. 5 Pier 6 Expansion Bearing ( Li, 2000) Although not with in the scope of work, URS noted other problem areas they observed in their report. None of the other expansion bearings were sliding and performing as intended requiring replacement of the expansion bearings Some of the girder ends were observed to have rust; however, no section loss was found therefore removing the rust and repainting would be a sufficient repair. Areas of concrete on the deck overhang were delaminating, so removing the delaminated piece and patching the area was recommended for the safety of the ve hicles travelling on Santa Fe Drive. Rust was visible on the bottom of pier caps for Pier 3 and 6, suggesting deteriorating reinforcement, exposing the

PAGE 38

! 26 reinforcement would be required to determine the extent of the corrosion. A vertical crack in the Pier 6 concrete cap cantilever was also observed and URS recommended running a section analysis to determine the cause and repair of the cap. Lastly, the space between the girder and the west abutment was a concern, requiring an expansion analysis on the ther mal movement to determine adequate spacing. 3.3.2.3 2001 Movement and Stress Study Report Based on URS's recommendations, CCD contracted with them to complete a movement and stress study. Between March 2000 and March 2001, URS performed four measurements to determine the movement of Pier 6. Other organizations were contracted to aid in the measurements which included Atkinson Noland & Associates for the condition of the cracked pier cap a t Pier 6, and the University of Colorado Den ver, lead by Dr. Kevin Rens, for the condition of the corroded steel girders. URS utilized a standard surveying approach to collect data for the movement of Pier 6 (Li, 2001) Tapes mounted to the pier cap and c olumn were read from set points. From the readings during the four visits, the top of the column was found to be deflecting in the east west direction creating a moment of 50% of t he column's flexural capacity. It was recommended to check the column when new expansion bearings

PAGE 39

! 27 are installed. The deflection in the north south direction was found to be negligible. Atkinson Noland & Associates conducted measurements on the crack in the cantilever cap of Pier 6 using tomography to determine the s ize and lo cation of the cracks (Rens & Transue, 2002) The vertical crack was discovered to be approximately 8 inches deep at the top of the cap and completely through at the lower portion of the cap refer to Figure 3.6 URS took this data and analyzed the tensio n. The pier cap was determined to have sufficient capacity remaining; however, it was recommended to seal or patch the crack to prevent further damage.

PAGE 40

! 28 Figure 3. 6 Deteriorated Concrete Pier Cap Dr. Kevin Re ns and his research assistants from the University of Colorado Denver took measurements on the corroded steel girders using an ultrasonic testing method to determine the amount of steel lost. The measurements gathered revealed that 21% of the steel web was lost at the worst location (Li, 2001) Even though there was a loss in the section, the web thickness remaining was still adequate based on the HS20 live load requirements. Having an adequate section repairing the girders would consist of cleaning off the rust and repainting the steel.

PAGE 41

! 29 3. 3.2.4 2009 Condition Inspection As the condition of the Evans Bridge worsened between 2000 an d 2008, CCD contracted Felsburg Holt & Ullevig (FHU) to complete a condition Inspection report in 2009. FHU was to also provide recommendations to rehabilitate the bridge to a 30% level. The findings and recommendations are discussed in chapter 4.

PAGE 42

! 30 4 Rehabilitation Project 4 .1 Project Initiation CCD's biannual inspections from 2000 through 2008 showed that the Evans Bridge was deteriorating and needed at least $31,800 in repairs. The 2008 inspection prompted repairs to the steel girders below the abutments of the adjoining ramps to Santa Fe Drive because of the severity of the corrosion. Due to the deteriorating condition of the bridge, CCD contracted with FHU in 2009 to complete a thorough condition inspection The purpose of this inspection wa s to determine the actual condition of both structural and non structural components, and to make repair recommendations for a rehabilitation project. 4.2 Visual Inspection FHU contracted with LONCO to aid in the inspection. The inspection began on June 8, 2009, and took most of two weeks to complete, although some portions of the inspection were not completed until September 2009 (Felsburg et al, 2009). All elements were inspected for code compliance as well as the general condition. Recommendations for the repairs to the above the deck portion of the bridge was to replace the asphalt overlay, concrete median, and concrete barrier walls due to poor or deteriorating conditions. Replacement of the drainage system was recommended as it was found to be clog ged and no longer functioning. The

PAGE 43

! 31 railings on the concrete barrier walls did not show significant damage, but replacement was recommended since they did no t meet current code standards. The inspection of the concrete deck was based on findings from the underside of the deck, since the topside is currently covered with asphalt. Areas under deck displayed cracking, spalling, and efflorescence. Most of the deteriorated areas were under the expansion joints on the north and south edges o f the bridge. Repairing the damaged areas was recommended. A previous inspection by URS in 2000 recommended replacing all of the expansion bearings as they were not functioning as intended due to corrosion and deterioration. As the bearings had not yet b een replaced and are still not functioning, FHU recommended that all expansion bearing s be replaced. The final area inspected was the steel girders as the girders were in a corroding condition near the ramp abutments discovered in the 2008 inspection. O utside of the rust locations the girders appeared to be in good condition. FHU took note of the fatigue critical locations at the ends of the partial length cover plates. Due to the age of the bridge FHU and CCD decided to investigate the condition of the fatigue sensitive details to determine the remaining fatigue life of the girders in order to insure an additional 20 years of life to the bridge.

PAGE 44

! 32 5 Visual Inspection and Fatigue Life Design 5 .1 Traffic Counts LONCO with the help of CCD collected traffic counts on the Evans Bridge in May 2009. From the collected data LONCO determined the worst case scenario of truck traffic across both the 80' and 95' bridge spans. The worst case for the 80' span was 1,510 trucks which occurred in the east bound direction on the west side of the bridge (over spans 1, 2, and 3) prior to the traffic enter ing onto Santa Fe Drive ( Figure 5. 1 ) which accounted for 11% of the total traffic. For the 95' span, the worst case scenario was in the west bound direction a t 1,189 trucks which accounted for 7.8% of the total traffic. Figure 5.1 Evans Bridge 2009 ADTT Counts ( Adapted from Felsburg et al 2009) 5.2 Bridge Girder Modeling The girder system of the bridge has partial length cover plates on various portions of each girder. There are a variety of cover plate configurations including; sections of girders which have cover plates on the top and bottom

PAGE 45

! 33 flanges, sections that have cover plates on the bottom flange only, and sections which create a composite section with the concrete deck above. Due to the complexities of these sections and a moving live load, more accurate results w ill be produced by modeling both the 80' and 95' 3 span girders in a structural modeling softw are. The software being used to evaluate the beam for the maximum positive and negative moment stresses is STAAD As specified in the LRFD an HS 20 design truck load is used for fatigue analysis. T he HS 20 design truck has a front axel load of 8 kips spaced 14' from the second axel and the two rear axels are spaced at 30' with 32 kips on each axel ( AASHTO 2012 pg. 3 28) The HS 20 design truck load is placed on the girders in the STAAD model No load factors are applied to the model, as onl y the maximum positive and negative moments of each detail location are desired in the output. Table 5. 1 in S ection 5.3.3 below shows the maximum positive and negative moments calculated on the beam at the specified locations from the modeling software. 5.3 Fatigue Analysis 5.3.1 Stress Range As discussed in 2.1, fatigue failure is due to repeated cycles of stress occurring above the fatigue threshold, which is significantly less than the amount of stress required to cause yielding B ecause of this fatigue occurs within the elastic range. The stress, at the girder details is a function of the bending moment, M over the elastic section modulus, S ( Equation 5.1 )

PAGE 46

! 34 ! ! 5.1 Section moduli for the top and bottom of steel for each different detail were calculated, as shown in Appendix A and B for calculations. Due to the continuous 3 span condition of the girders, the STAAD model provided the positive and negative bending moments The negative and positive stresses for the to p and bottom flanges of the girder were calculated using Equation 5.1. The live load stress range due to the passage of fatigue load f was then determined for each flange from the calculated positive and negative stresses (refer to Table 5. 1 in section 5.3.3 ) 5.3.2 Nominal Fatigue Resistance Two reductions are applied to the stress range to determine the nominal fatigue resistance, ( F) n the fatigue live load factor, LL and the live load distribution factor for one traffic lane, g Equation 5. 2 (AASHTO, 2012 ). ! ! ! !! ! 5.2 5.3.2.1 Fatigue Live Load Factor The Fat igue category II is defined as Fatigue and fracture load combination related to finite load induced fatigue life (AASHTO, 201 2 pg. 3 11). The purpose of this analysis is to determine the load induced finite fatigue life making

PAGE 47

! 35 Fatigue II the relevant category, as Fatigue I is used for "infinite load induced fatigue" (AASHTO, 2012 pg. 3 10). As demonstrated by the live load factor table, LL =0.75 for Fatigue II (AASHTO, 2012 pg. 3 13). 5.3.2.2 Live Load Distribution Factor Moment and shear live load distribution need to be computed for both interior and exterior beams. Each of the four distributions should be checked for one design lane loade d and two or more design lanes loaded. This is not always true as a clause states that for fatigue design the live load distribution factor should be calculated for only one design lane loaded and that the multiple presence factor of 1.2 included in the provided equations is to be removed (AASHTO, 2012 3 18). As discussed in section 5.3.1, the stresses being calculated are coming from the positive and negative moments at the specified locations provided by t he structural modeling software, meaning that only the moment distribution load factor need be checked. Instead of eight calculations to determine the governing live load distribution factor, g only two need be considered which is moment distribution for one design lane for an interior and for an ex terior girder. 5.3.2.2.1 Moment Distribution on Exterior Girders Moment distribution on exterior girders due to one design lane loaded is calculated using the lever rule. The lever rule assumes the deck is simply supported between the exterior beam and the adjacent interior beam, and a hinge at the interior beam so no additional forces transfer. Live load from the

PAGE 48

! 36 design truck is applied 2' from the curb at the first truck wheel and the wheels are spaced at 6' with an axial force applied at both tires. Summing the moments around the interior beam provides the reaction at the exterior beam. Ignoring the actual axial load and solving for the reaction at the exterior beam in terms of variable P provides a ratio of P ; this ratio is the distribution factor applied to the exterior girder. In the case of the Evans Bridge the exterior girder is located 1' 5" from the outside face of the bridge, the girders are spaced at 6' 10" on center, and the outside face of the bridge to the end of the sidewa lk measures 7' 8" ( refer to Figure 5 2 below ) The question here becomes, if there is no truck load on the span between the exterior and adjacent interior girder, does the distribution facto r matter at the exterior girder ? A distr ibution load can be solved for usi ng the pedestrian load, however, the pedestrian load will be mini mal compared to a truck load. By this rational e the interior girder s will have more load than the exterior girder and since the bridge is being evaluated o n a design truck and not pedestrian traffic, the calculated distribution factor should be based on the moment distribution of one design lane loaded for an interior girder.

PAGE 49

! 37 Figure 5.2 Evans Bridge Cross Section ( Felsburg et al 2009) 5.3.2.2.2 Moment Distribution on Interior Girders The live load distribution factor for interior girder s g is a function of the longitudinal stiffness parameter, K g girder spacing, S girder length, L and slab thickness, t s (AASHTO, 2012 pg. 4 32 ) W here the stiffness parameter is a function of the girder section properties, distance between centers of gravity, the modular ratio of the girder and concrete deck, and Equation 5.3 through 5.5 The stiffness parameter determines ho w stiff the girder is r elative to the deck. ! ! ! ! ! 5.3 Where: A = Cross Sectional Area of the Girder I = Moment of Inertia of the Girder e g = Distance between the Deck and Girder Centers of Gravity

PAGE 50

! 38 n = Modular Ratio of Girder and Deck ! ! ! 5.4 Substituting Equation 5.4 into 5.3 gives: ! ! ! ! ! ! 5.5 Once the longitudinal stiffness parameter has been determined the distribution factor can be calculated using the equation for one design lane loaded for a deck and beam br idge configuration ( Equation 5.6 ) ! ! !" ! !" ! ! ! ! ! !" ! ! ! 5.6 The multiple presence factor mentioned in section 5.3.2.2 needs to be removed from the distribution factor. Dividing the distribution factor by the 1.2 multiple presence factor gives a final distribution factor of 0.34 for the 80' span and 0.33 for the 95 span. 5.3.3 Infinite Fatigue Life Infinite fatigue life occurs when the maximum stress, ( f) max is less than the fatigue threshold, ( F) TH of the specific detail category. The maximum stress is

PAGE 51

! 39 a function of the effective stress, ( f) eff which is a function of the nominal stress, ( F) n calculated in section 5.3.2 ( refer to Equation 5.7 through 5.9 ) In this check AASHTO assumes that no load applied will be greater than two times the calculated effective stress, providing a factor of safe ty for determining whether a detail has infinite life. ! !"# ! ! !"" 5.7 !" !"" ! !" 5.8 Where: R s = Partial Load Factor ( AASHTO 201 1 pg. 7 3 ) When designing versus evaluating a bridge from collected data, the partial load factor is 1.0, making the effective stress the same as the nominal stress. However, if field data is collected the partial load factor can reduce the nominal stress by as much as 15%. This reduction removes the factor of safety in the AASHTO design calculations, because there is little uncertainty in nominal stress produced by actual data ( Chotickai and Bowman, 2006 ) Substituting Equation 5.8 into 5.7 gives: ! !"# ! ! ! 5.9

PAGE 52

! 40 The detail cate gories relevant to the 80' span are B, C, C', and E, with fatigue thresholds of 16 ksi, 10 ksi, 12 ksi, and 4.5 ksi respectively Only two detail categories are used for the 95' span, B and E', with 16 ksi, and 2.6 ksi fatigue thresholds. After solving for the maximum stress for each detail the maximum stress is checked against the fatigue threshold to determine if the detail section has infinite life or needs to be checked for finite fatigue life. The only detail categories that did not have infinite life were E for the 80' span, an d E' for th e 95' span. Refer to Tables 5.1 and 5.2 below for the data for the determination of infinite fatigue life on the bottom girder of the 80' span. Refer to Appendix C and D for complete details on the top and bottom flanges of the 80' and 95' spa ns.

PAGE 53

! 41 Table 5 1 80' Span Girder Stress Distribution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

PAGE 54

! 42 Table 5 2 80' Span Girder Bottom Flange Fatigue Life Check 5.3.4 Finite Fatigue Life From the infinite fatigue life check in section 5.3.3 it was determined that all E and E' detail categories for the 80' and 95' spans need to be checked for finite fatigue life For the case of the Evans Bridge detail category E and E' both occur at the end of the partial length cover plates, but there is a difference in the flange thickness of the girders. The 80' span girder is a W36x135 with a flange thickness of 0.79 inches, and the 95' span girder is a W36x182 with a flange thickness of 1.18 inches. For a partial length cover plate the detail categ ory changes from E to E' when the flange thickness of the W sha pe is greater than 0.8 inches. Finite fatigue life is derived from the equation used for design of fatigue resistance in which the nominal stress is a function of the detail category constant, A over the number of cycles, N that will cause the detail to fail due to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

PAGE 55

! 43 fatigue. Equa tions 5.10 through 5.13 derive the design equation to calculate how many years, Y the detail will last before failure. !" ! ! ! 5.10 Where: ! !"# !" !"## !" 5.11 Where: n = Cycles per Truck Passage (LRFD, 2012 pg. 6 51 ) Substituting Equation 5.11 into Equation 5.10 gives: !" ! !"# !" !"## !" ! 5.12 Solving for the number of years, Y gives: ! !"# !"## !" !" ! 5.13

PAGE 56

! 44 The AASHTO Manual for Bridge Evaluation uses Equation 5.13 with two modifications to determine the finite fatigue life. First, the effective stress is used in lieu the nominal stress, which per Equation 5.8 is the nominal resistance multiplied by the partial load factor. When designing versus evaluating a bridge from collected data the partial load factor is 1.0, making the effective stress the same as the nominal stress. The second modification is the multiplica tion of the constant A by the resistance factor, R R which is dependent upon the detail category. There are three levels for the resistance factor : the minimum fatigue life, the evaluation fatigue life, and the mean fatigue life. For all minimum fatigue life the resistance factor equals 1.0, which is the resistance for design. Equation 5.14 shows Equation 5.13 with the partial load and resistance factors. Both the partial load factor and the resistance factor will increase the number of years a structu ral member will last when evaluating members for fatigue life due to that collected data of how the member is actually responding will provide more accurate results and factors of safety can be reduced. ! ! !"# !"## !" ! !" ! 5.14 Since the bridge being evaluated for fatigue life and not being designed the resistance factor, R R for the minimum, evaluation, and mean are considered. Using Equation 5.14 the design fatigue life can be determined from the traffic counts and nominal st ress with varyin g fatigue resistance. Table s 5.3 and 5. 4 below show the minimum, e valuation, and mean fatigue lives for the bottom

PAGE 57

! 45 flange of the 80' and 95' span s From these calculations the minimum that the 80' span girder would last is 4 8 years, whereas the mean life gives the girder 77 years. The 95' span has a minimum fatigue life of 25 years ( which is not possible since the bridge is already 40 years old ) and the mean fatigue life is calculated at 63 years. Refer to Appendix C and D for more details. Table 5 3 80' Span Girder Bottom Flange Fatigue Life Table 5 4 95' Span Girder Bottom Flange Fatigue Life !"#$%&'( )*+,%-.'/% !0""'., 1'2#,*'$% 34"5 )5,#*6%7#, 85+06, 9%:;+* < = >? 5?? @ /*$ %%%%%%%%% 8 8 AB @ 5C#6 % 8 8 AD#.*5+ @ /5#$ % 8 8 AD#.*5+ B BE(F !,0G H I$?*$*,5 B(EJKLBJ <(JJ &M9 &M9 &M9 B BF KNO K 7PK7Q B(BJKLJR E(SF BTJ EJU EFT B ? 5?? @ /*$ %%%%%%%%% 8 8 AB @ 5C#6 % 8 8 AD#.*5+ @ /5#$ % 8 8 AD#.*5+ E BF GHI GJ 7KG7L <(MNGONP Q(BF BNR BFP QFQ E
PAGE 58

! 46 6 Strain Transducer Testing Procedures 6.1 Strain Transducer History Hunter Christie originally developed the Wheatstone bridge circuit in 1833, although Charles Wheatstone popularized the circuit, which is why the circuit was named the Wheatstone Bridge ( Stefanescu, 2011). The Wheatstone Bridge circuit utilizes the force applied to change the voltage of the circuit which is then calculated back into force for the data output (Desai 2007). Strain transducers were developed d ue t o the simplicity and sensitivity of this circuit configuration T he pile driving industry began using Wheatstone Bridge circuit strain transducers t o record the strains of the piles in 1970 (BDI Operations Manual 2011) 6 .2 Strain Transducer Development Bridge Di agnostics Incorporated (BDI) has further developed the strain transducer used by the pile driving industry BDI Strain Transducer ST350, to collect data for dynamic and event driven stresses of bridge and building structural members through means of nondestructive testing shown in Figure 6.1 The m ounting of the transducers to steel uses an adhesive making the process entirely nondestructive. The transducer a re built to be a manageable size and fairly inconspicuous, m easuring 4.35 inches (110.5 mm) long by 1.23 inches (31.2 mm) wide and .51 inches (13 mm) thick

PAGE 59

! 47 Figure 6.1 BDI ST350 Strain Transducer The ST350 transducers have a flexible design so that large strains can be measured from the structural member without pl acing much axial load on the transducer. Only live load strains are recorded, since the dead load is a static load rather than a dynamic load The dynam ic strain data from an event occurs in such a short time frame that thermal movements of the structural member and transducer are assumed to be negligible. 6.3 Transducer Ins tallation On March 8, 2011, BDI installed 20 ST350 strain transducers to the bottom flanges of the steel girders on spans 1 and 2 of the west e nd of the Evans Bridge shown in Figure 6.2 FHU predetermined that the fatigue prone locations in the girders are at the ends of the partial length cover plates and installed the

PAGE 60

! 48 transducer s within 4 inches of the ends of the cover plates, as shown in F igure 6.3. Figure 6.2 Strain Transducer Locations ( Felsburg et al 2011)

PAGE 61

! 49 Figure 6.3 Transducer Location to Partial Cover Plate (Felsburg et al 2011) Since the strain needed to be read for the span of the beam and the bottom of the girder was accessible, the transducers were aligned parallel to the length of the girder and positioned in the center of the flange 4 inches from the ends of the partial length cover plates as shown in Figure 6. 3 Dirt, paint, oxidation and any other contamina nts were removed by lightly grinding the surface before installation to guarantee adhesion of the transducer. Guide lines were then drawn on the mounting surface for accurate alignment, as the transducer will only read strain in the axis in which it is aligned. Measurements were taken to the center of the flange and marked where the center of the transducer should be. S mall lines were then marked perpendicular to the length of the girder 1 inches on either side of the transducer midpoint. These marks indicated the center of the bolt holes. To e nsure proper alignment of the transducer bolt hole s to the marks on the girder, the transducer tab bolts were first plac ed through the transducer and the nuts tighten ed prior to adhering the tab s to the steel.

PAGE 62

! 50 Once the tabs were mounted to the transducer a small amount of adhesive was applied to the bottom of the tabs. T he tabs, with the transducer attached, were then pl aced on to the locations previously marked on the steel and remove d. In this step, some of the adhesive was placed onto the girder and then a small amount of adhesive accelerator was sprayed on to the adhesive left on the steel while the transducer and tabs were mounted to the same location as previously placed. T he adhesive accelerator reduces the amount of human error in the alignment of the system as the transducer only need s to be held in place for 15 20 seconds for adhesion The fin al process included a luminum covers with a foam board insulation being mounted around each transducer to protect the system while monitoring the bridge as seen in Figure 6. 4 and Figure 6.5 Figure 6.4 Aluminum Cover Around Transducer

PAGE 63

! 51 Figure 6. 5 14 of 20 Installed Transducers BDI's t ransducers are all prewired and quickly connect to their structural monitoring system where the data is recorded. The structural monitoring system was mounted to the steel channels above the concrete piers using clamps to ensure an entirely nondestructive testing sy stem, shown in Figure 6. 6 A lock box containing a 12 volt battery providing power to the monitoring system was mounted to the steel in a similar manner as the monitoring system shown in Figure 6. 7 BDI collected the data logged by the monitoring system wirelessly on a cell phone and downloaded the strain readings regularly to the office computer system.

PAGE 64

! 52 Figure 6. 6 Structural Monitoring System Figure 6. 7 Structural Monitoring System Power Source

PAGE 65

! 53 6.4 Transducer Removal On April 12, 2011, BDI removed the ST350 strain transducers and the supporting system from the Evans Bridge. The order of the removal process is important to keep the transducers from b eing damaged and useful for further projects. Prior to removing the transducers the aluminum cover was removed. During installation the adhesive tabs were mounted to the transducers first and then mounted to the girders to e nsure accuracy of placement. However, during disassembly the transducers were first removed from the tabs prior to removing the tabs from the steel. After the transducers and tabs were removed the monitoring system including the battery and housing boxes were removed. The disassembly of the system was quick taking approximately an hour to complete.

PAGE 66

! 54 7 Strain Transducer Results and Analysis 7 .1 Traffic Counts 7.1.1 Traffic Data BDI took traffic counts March 8, 2011 through March 25, 2011, while also collecting data from the strain transducers placed on the girders of the Evans Bridge. These supplemental traffic counts were collected to verify the counts collected for the 2009 Condition Inspection Report. The data collected was separated into the following categories: bikes, ca rs / trailers, two axle four tire trucks, buses, two axle six tire trucks, three axle single unit trucks, four axle single unit trucks, five axle single unit trucks, five axle double unit trucks, six axle double unit truck s and larger, anything smaller than six a xle multi unit trucks and six axle multi unit trucks The largest recorded total traffic count of those days was Friday, March 11, 2011, with a total 16,009 vehicles and 1 480 vehicles larger than two axle four tire trucks. This was not the highest truck count as that number was exceeded on four consecutive days from Tuesday, March 15, 2011, through Friday, March 18, 2011, with counts of 1,535, 1,536, 1,495, and 1,498 respectively. Considering t he timing of these counts there could be correlation in the increase in truck traffic to the amount of alcohol dis tribution for Saint Patrick's Day holiday and the following weekend. Refer to Appendi x E for more data on the traffic counts collected by BDI.

PAGE 67

! 55 7.1.2 Average Daily Truck Traffic Average Daily Truck Traffic (ADTT) is utilized in calculating the fatigue life of a bridg e. From the 2009 Condition Inspection Report the ADTT was 1,510 trucks per day in one direction. In order to verify the accuracy of the previous counts, BDI collecte d additional traffic counts referenced in 7.1.1 T he three highest consecutive days of truck traffic to calculate the ADTT were 1,535, 1,536, and 1,495, averaging 1,522 trucks per day in one direction. For consistency, it was assumed that the count of 1, 522 trucks was close enough to u tilize the same ADTT of 1,510 trucks used in the 2009 Condition I nspection Report 7.2 Control Test 7.2.1 Control Test On March 24, 2011, between 6:30 AM and 7:00 AM a control test was conducted on the Evans Bridge. A tandem axle loaded truck of known weight, 51,560 lbs, was driven across the bridge while all other traffic on Evans was stopped on either side of the ramps leading up to the bridge and the traffic on S anta Fe Drive was diverted to the next exit ( refer to Figure 7 .1 through Figure 7.4 ) The purpose of this test was to determine how much a single truck would stress the bridge girders.

PAGE 68

! 56 Figure 7.1 Truck at Base of Evans Bridge for Control Test Figure 7.2 Truck Climbing Ramp of Evans Bridge for Control Test

PAGE 69

! 57 Figure 7.3 Truck Approaching Strain Transducers During Control Test Figure 7.4 Truck Completing Control Test Four passes were completed with the truck, all of which were completed in the eastbound direction over the bridge above the strain transducers The truck

PAGE 70

! 58 was at a slow "crawl" speed in each lane for two of the tests, and then a high speed test was completed in each lane as well. During these tests the structural monitoring system was set up to record event data. 7. 2 .2 Control Test Results Event data was recorded for each of the four control tests with the structural monitoring system record ing the stress of each transducer at 0.02 second intervals. For each one second of t ime 50 data points were documented for each transducer. Each test logged anywhere from 60,000 to 80,000 data points, which can be difficult to evaluate, but plotting the points provide d a good visual representation of what occurred during the tests. As the truck passe d over the transducers, tension (shown as positive) was always read first since the bending moment is placing the bottom flange of the girder in tension. Once the truck passe d and the girder reverberate d back into its original shape the bo ttom flange of the girder w ent into compression (shown as negative). Although the magnitude of the compressive stress was less than that of the tensile stress, it was still a noticeable force.

PAGE 71

! 59 During Test 1 the truck was at a "crawl" speed in the exte rior lane and at approximately 28 seconds into the test the transducers began to record stresses beyond the normal vibrations of the bridge. Transducer J1 recorded the maximum stress of 3.68 ksi tension before recoiling into 1.02 ksi of compression. The tension and compression stresses at transducer J1 have the maximum stress range for Test 1 of 4.71 ksi ; refer to Figure 7. 5 for the plot of Test 1 transducers F1 through K1. Figure 7. 5 Control Test 1 Results for Transducers F1 K1

PAGE 72

! 60 During Test 2 the truck was also at a slow speed, but drove in the interior eastbound lane. The maximum stress range of 4.42 ksi occurred at transducer I1, with the maximum tensile stress of 3.53 ksi, and the maximum compressive stress of 0.89 ksi. Refer to Fig ure 7 .6 for the plot of Test 2 for transducers F1 through K1. Figure 7.6 Control Test 2 Results for Transducers F1 K1

PAGE 73

! 61 The third test was completed in the interior eastbound lane at a high speed, relative to the speed limit. Similar to Test 2, which was also completed in the interior lane, Transducer I1 had the maximum recorded stress range of 4.35 ksi, where 3.36 ksi was in tension and 0.99 ksi was in compression. See Figure 7 .7 below for the plot of Test 3 for transducers F1 through J1. Figure 7.7 Control Test 3 Results for Transducers F1 K1

PAGE 74

! 62 Test 4 was completed in the exterior lane at a high speed. Transducer J1 reached a tensile stress of 3.55 ksi and a compressive stress of 0.95, with the maximum stress range of 4.50 ksi. These findings were consistent with those of Test 1, which was also conducted in the exterior eastbound lane. Refer to Figure 7 .8 for the plotted resul ts of Tes t 4. Test results for the four control tests are summarized in Table 7.1. Figure 7.8 Control Test 4 Results for Transducers F1 K1

PAGE 75

! 63 Table 7.1 Control Test Results Summary All four of the tests resulted in a stress range within 0.2 ksi of the 4.5 ksi threshold of the 80' span girders Since the speed of the truck d id not seem to have an affect on the stress recorded by the transducers, the overall weight of the loaded truck was determined as the cause of the stress range reaching the threshold. From these findings it can be concluded that a n unloaded tandem truck wou ld not produce these values; therefore it is the passage of loaded trucks that will affect the girder fatigue life. The control test also proves the number of cycles per passage, n of a truck. For a 3 span continuous girder longer than 40' there are two values for n near an interior support and elsewhere. The strain transducers were installed near the center of the first bay. Based on Figures 7.5 through 7.8, the number of cycles read by each truck passage was one, where the peak of the tension to the peak of the compression stresses is read as one cycle. This is consistent with AASHTO stating n=1.0 for anywhere in multiple span girders that is not adjacent to an interior support. !"#$%&' ()#$* +%,-."##$%&' ()#$* /01$,2,' 34."##'50&6"' ()#$* !.0˘". 9:;< =:>? @:A> B= 9:C9 >::DD @:9C E= $ 9:CC >:DC @:C> B= %&'()&*+ ,-.(

PAGE 76

! 64 7. 3 Stress Cycles 7.3 .1 Stress Cycle Counts BDI collected strain data from March 8, 2011, through April 11, 2011. The structural monitoring system was programmed to record the number of stress cycles per hour that ranged between 1 ksi and 11 ksi in .5 ksi increments and stress cycles greater than 11 ksi ( refer to Table 7. 2 ) These stress ranges correlate to the ranges the transducer reaches durin g a cycle, not the actual stress reached. For example, during a cycle the transducer could read 2 ksi and 3 ksi, this would place the cycle within the 5 ksi range. The stress c ycles were recorded and logged separately for each of the 20 strain transducers. From the 40 516,236 cycles recorded, 97.1% occurred within the 1 ksi to 1.5 ksi range.

PAGE 77

! 65 Table 7. 2 Stress Cycle Count Summary !"#$!"% !"%$&"# &"#$&"% &"%$'"# '"#$'"% '"%$("# ("#$("% ("%$%"# %"#$%"% %"%$)"# )"#$)"% )"%$*"# *"#$*"% *"%$+"# +"#$+"% +"%$,"# ,"#$,"% ,"%$!#"# !#"#$!#"% !#"%$!!"# -!! .! !""#$%& $%"'% '&(# (&") !$"# '*' *!" )'& '$ %$ %$ !! ! & & & & & & /! )))'%&) #$$)( !!%#& ())* %)(& !"#' *(% )'$ )*" )$& !'% #' $! )% !( ( ) ! /!01 !$(%!!) %&'$( *)%! )%#! $%) ((( )%% "& )& !$ ) ) & & & & & & & & 2! )))"(#( *&'$! #()* (!)" !%"% "&) ()' )(* '! $$ )& !& ) $ % & & & & & & 3! )!!$)"& #&*%! ')%# )!'# !)#' "$' %&( !"( '! *$ (& !$ !& ) & & & & & 4! )$&!"') '&*"* ""'& )&"% "') %"' !#% !)! !*$ !&% %$ !) # ) % & % & & & & 5! )%(&&"" #%%&# ($$# !!&& ()# !"% #$ !$& !%' %% !& % % ) % & & & & & & .& !*!&)"$ %($%" *#"% )!#' #)% (*% !$% %! # % ! & & & & & & & & & /& !"'"&*( %#'"& $"*) %("" "$* %%" %'& !$& %& !% ( ) & & & & & & & & /&01 !*%%)!! !*&"' %)#$ *$# )#' %! ( ( & & & & & & & & & & & & & 2& !"!#&)( (*&'* ")*$ )*%' "#" $!' !*! *& !$ # & & & & & & & & & & & 3& !""(#"! $"#($ (!$! !(*$ "%) )!( !%( "& )% !) & & & & & & & & & & 4& )*#'($! $&$"" %$#) #'& %&& )!! !"# %) !& & % & & & & & & & & & 5& )(#&*$* %&$$$ !'() $%) !$$ )(* ## !! ) ) & & & & & & & & & & .' )!$!$)' %$&!! $#&' !"&& *"% !*# $# !( ! & & & & & & & & & & & /' !**$$$( %"$($ *'*( )'!$ #$* (*& )(" *' )( !( ) & & & & & & & & & 2' !*!!"(" %'##! *$#& !#&$ "$% %"$ !%% ($ !$ $ & & & & & & & & & & 3' !##&"$% (&&!( %*(# !%$( $!! )&$ !&( )( # $ & & & & & & & & & & & 4' !$&)#*) %*''% %&%# "*$ )*$ )%$ '# %) % $ & & & & & & & & & & & 5' )&'"!!! )$*'! !*#$ (&' !)' )&* !&! !& $ & & & & & & & & & & & 6789:;8<=>9?@7 /;<=9AB0;C7B8

PAGE 78

! 66 As previously discussed in 5. 3.4 the fatigue threshold for a beam with a flange less than 0.8 inches at the end of a cover plate is 4.5 ksi (AASHTO 2012 ) During the testing 4,211 stress cycles were recorded over the 4.5 ksi threshold, equaling 0.01% of the total counted cycles. Only once did the monitoring sy stem record a stress cycle over 11 ksi which occurred on March 31, 2011 between 10:00 and 11: 00a.m. and was recorded on transducer G1 ( refer to figure 7.9 ) Transducer G1 was located on the first span approximately 50 feet from the w est end, and the girder is located in the center of the bridge

PAGE 79

! 67 Figure 7.9 Strain Transducer Locations ( Felsburg et al 2011) 7.3 .2 Stress Cycle Data Analysis for 80' Girder Span The data collected was first totaled into the number of times each strain transducers reached a specific stress range, 1 ksi to 1.5 ksi, 1.5 ksi to 2 ksi, etc., during the 31 day data collection period ; refer to Table 7.2 and Appendix F for a summary. After the data was organized in to a more manageable way, the data was totaled again in two separate manners The first was the total of the cycle

PAGE 80

! 68 count s for a particular stress range In this model 1 ksi to 1.5 ksi, 1.5 ksi to 2 ksi, etc ., were calculated, disregarding the specific transducer correlated to the count From the total cycle counts per stress range the percentage of occurrences over the 4.5 ksi threshold were calculated. In the second method the number of occurrences for a specific transdu cer was totaled, disregarding the particular stress range that the stress cycle occurred in The total cycle count per transducer was used to calculate the percentage of cycles at a particular stress range, which provides i Estimating th e finite fatigue life of an element, a s discussed in section 5. 3.4 is a function of the detail category constant A the average number of trucks in one direction per day in a single lane, (ADTT) SL and the effective fatigue threshold, ( f) eff ; refer to Equation 7.1 ( AASHTO 2011 ) Previously determined, the detail category for a W36x135 at the end of a partial length cover plate is E, giving the constant, A of 11x10 8 ksi 3 ( AASHTO 2012). ! ! !"# !"## !" ! !"" 7.1 Where: Y = Number of Years of a Structural Element Due to Fatigue R R = Resistance Factor for Minimum Fatigue Life n = Number of Stress Rang e Cycles per Truck Passage

PAGE 81

! 69 Solving for the finite fatigue life of the girders R R is set as 1.0 for the minimum life for all detail categories which will produce the most conservative evaluation because it is assuming a 2% probability of failure The number of stress ran ge cycles per truck passage, n was taken as 1.0 since the tran sducers we re located in the middle of the girder span girder and not near a support. (ADTT) SL is the average daily truck traffic in a single lane, which is the product of the ADTT count, and the number of lanes available to trucks in one direction, p (AASHTO 2012 ). Each direction of the Evans Bridge has two lanes available to trucks ; therefore p is 0.85. U sing the ADTT of 1,510 as previously determined, (ADTT) SL is calculated at 1,284 trucks in one lane per day After determining the ( ADTT ) SL only one variable remains in estimating the finite fatigue life of one of the girders t he effective stress ( f) eff In the collected data the effective stress is determined from the particular stress range, f i and the percentage of cycles at the particul ar stress range, i Equation 7.2 ( AASHTO 2011) T he percentage of cycles at a particular stress range for a specific transducer were determined from the number of cycles that occurred within a stress range over the total cycles counted for the transducer ; refer to Appendix F. For the particular stress r ange the value was taken as the maximum of the predetermined range for example, a stress range of 1.5 ksi to 2 ksi would use a f i of 2 ksi A ssuming all particular stress ranges are at the max imum end of the range more conservative results will be produced More accurate results would be produced if smaller stress ranges were programmed into the structural monitoring system ; however, this would c reate more data

PAGE 82

! 70 points and create a more intensi ve analysis. Since the fatigue life calculation is only an e stimate it is reasonable to have stress cycle rang es with 0.5 ksi increments. ! !"" ! ! ! ! ! ! 7.2 Where: R s = Stress Range Estimate Partial Load Factor The Stress Range Estimate Partial Load Factor, R s can be taken as 0.85, since the fatigue life evaluation is using stress ranges collected from field measured strains (AASHTO, 2011) This reduction removes the factor of safety in the AASHTO design calculations, because there is little uncertainty in nominal stress produced by actual data ( C hotickai and Bowman, 2006 ). The partial load factor can be taken for both the minimum and evaluation fatigue life calculations. Calculating the mean fatigue life for all scenarios re quires the partial load factor to be 1.0, which will decrease the amount of years compared to that of the minimum and evaluation fatigue lives. However, the resistance factor, R R applied in equation 7.1 allows an increase for the mean fatigue life for de tail category E of 1.6. As discussed in 5 .3.4 this factor accounts for the evaluation fatigue life being one standard deviation below the mean and the minimum fatigue life being two standard deviations below the mean. Anywhere from 95% to 99% of the reco rded stress cycles for each transducer occurred between 1 ksi and 1.5 ksi. The high percentage of low stress cycle

PAGE 83

! 71 occurrences skews the estimated fatigue life of the bridge When using the 1 to 1.5 ksi stress range the calculations estimate that one gi rder would last 982 years ( refer t o Table 7. 3 and Appendix F for more information ) This does not provide an accurate estimate of the actual finite fatigue life of a girder, as actual fatigue failure is a specific number of cycles that occur over the girder's fatigue threshold, a nd the estimated fatigue life provided by AASHTO is using a percentage of the cycles measured to calculate that number in terms of years Table 7. 3 Estimated Minimum Finite Life of 80' Span Girders with Minimum Stress Range o f 1.0 ksi to 1.5 ksi From the ADTT counts for the eastbound lanes the total number of vehicles counted from March 9, 2011 through March 24, 2011 was 228,290, 18,495 of which were trucks. The average number of stress cycles read by all the transducers during those 16 days was 848,365. This calculates to approximately !"# $ %& $ 3 ) 1/3 %& '&& ( !" )*++ )*,).)/ #" )*+/ )*,0 12#"$% )*+, )*,. ).3) &" )*+0 )*,) ).0. '" )*++ )*,).,) (" )*+0 )*,) ).0/ )" )*+, )*,. ).3. !* )*+, )*,. ).3) #* )*+0 )*,. ).+/ #*$% )*+) )*-1 )).0 &* )*+0 )*,) ).+, '* )*+, )*,. ).3. (* )*+)*-1 ).1)* )*+) )*-1 )).+ !+ )*+)*-1 ).23 #+ )*+0 )*,) ).+0 &+ )*+, )*,. ).3. '+ )*+)*-1 ).2) (+ )*+, )*,. )./2 )+ )*+) )*-1 )).+ #,-./01$,2314

PAGE 84

! 72 3.7 stress cycles per vehicle. The control test provided proof that only one cycle occurred for each passing truck ; therefore incorporating more stress cycles than vehicles in the evalua tion of fatigue life is inaccurate. The se additional cycles can be attributed to dynamic affects of the bridge and if incorporated into the fatigue life calculation, skew the remaining fatigue life calculation in an un conservative manner as show above in Table 7.3 By ignoring low stress cycles, the effective stress value increases, reducing the estimated fatigue life. Making it conservative to ignore low stress cycles. Determining the appropriate stress cycles to ignore or consider involves engineeri ng judgment, however can be compared to the controlled load test for validity Each individual vehicle is not likely to produce it's own stress cycle, as multiple vehicles are on the road at the same time especially during times of high traffic volumes C onsidering this, the number of overall stress cycles would decrease, but the stress cycle range s would increase due to additional load of multiple vehicles Of the total counted cycles 820,134 (97%) occurred in the 1 ksi to 1.5 ksi range, while 23,432 (2.8%) occurred in the 1.5 ksi to 2.0 ksi range. Ignoring stress levels from these two ranges leaves 4,827 cycles, which recorded stresses above 2 ksi. The controlled test truck weighed 51,560 pounds and induced a maximum stress cycle of 4.7 ksi. It is reasonable to assume events inducin g stress cycles greater than 2 ksi are capturing an event which is not merely dynamic effects within the bridge, but are loaded trucks or combinations of vehicles and should be considered in the fatigu e life calculation.

PAGE 85

! 73 With the removal of all cycles occurring below 2 ksi the m inimum fatigue life of 97 years is calculated for girder G as shown in Table 7. 4 Table 7. 4 Estimated Minimum Finite Life of 80' Span Girders with Minimum Stress Range of 2. 0 ksi to 2.5 ksi The minimum fatigue life calculated from the transducer data is 97 years as shown in Table 7. 4 As previously stated the minimum fatigue life uses a 0.85 partial load factor, R S as does the evaluation life. T his is due to the estimated stress range coming from actual data collected. However, the MBE requires all mean fatigue life evaluations to use a partial load factor of 1.0 for all scenarios. The resistance factor, R R for the minimum fatigue life of detai l category E is 1.0, whereas, the evaluation life resistance factor is 1.3, and the mean fatigue life resistance factor is 1.6. Because the partia l load factor and the resistance factor !"# $ %& $ 3 ) 1/3 %& '&& ( !" )*+) ,*-+,. #" )*/0 ,*12 23 #"$% ,*2) ,*/2 +.+ &" )*02 ,*-) +,2 '" )*03 ,*-+ +), (" )*01 ,*-, +)+ )" )*01 ,*-, +)+ !* ,*11 ,*/. +-0 #* )*0) ,*.1 +)3 #*$% ,*30 ,*)0 +2/ &* ,*20 ,*/+.3 '* ,*2,*., +/3 (* ,*2, ,*/1 +./ )* ,*2,*., +/3 !+ ,*32 ,*)3 +3. #+ ,*2/ ,*.0 +.+ &+ ,*13 ,*// +-, '+ ,*20 ,*/3 +.(+ ,*2+ ,*/3 +.)+ ,*21 ,*./ +// #,-./01$,2314

PAGE 86

! 74 differ for minimum, evaluation, and mean fatigue life calculations T ables 7. 5 and 7. 6 have been included to display the effects of the load factors. Table 7. 5 Estimated Evaluation Fatigue Life of 80' Span Girders with Minimum Stress Range of 2.0 ksi to 2.5 ksi !"# $ %& $ 3 ) 1/3 %& '&& ( !" )*++ )*++ ,+) #" )*-. )*-. ,)+ #"$% )*/. )*/. ,.0 &" )*+1 )*+1 ,+'" )*+, )*+, ,0, (" )*+) )*+) ,0, )" )*+) )*+) ,02 !* )*/3 )*/3 )2#* )*3)*3,0. #*$% )*12 )*12 )3) &* )*/+ )*/+ )23 '* )*3) )*3) ,., (* )*/)*/)22 )* )*3) )*3) ,., !+ )*10 )*10 ))#+ )*32 )*32 ,.+ &+ )*// )*// ),2 '+ )*/0 )*/0 )21 (+ )*/0 )*/0 )2) )+ )*3/ )*3/ ,-0 #,-./01$,2314

PAGE 87

! 75 Table 7. 6 Estimated Mean Fatigue Life of 80' Span Girders with Minimum Stress Range of 2.0 ksi to 2.5 ksi From the calculated fatigue lives, the minimum and mean fatigue lives are estimated to be 97 years and 95 years respectively. The evaluation fatigue life is estimated to be 126 years. Conservatively the fatigue life of the 80' span girders is 95 years ; however, the girders are currently under evaluation and not design, so it is reasonable to assume the fatigue life of the 80' span girders to be 126 years. 7.3.3. Stress Cycle Data Analysis for 9 5 Girder Span Average daily truck traffic, ADTT was used a s the maximum recorded during the 2009 counts, which was 1,189 trucks per day for the 95' span sections, since additional counts were not conducted during the 2011 analysis. The number of !"# $ %& $ 3 ) 1/3 %& '&& ( !" )*+) )*+) +,, #" )*-. )*-. /0 #"$% ,*/) ,*/) +-/ &" )*./ )*./ +,1 '" )*.1 )*.1 +,/ (" )*.2 )*.2 +,/ )" )*.2 )*.2 +,/ !* ,*22 ,*22 +01 #* )*.) )*.) +)0 #*$% ,*1. ,*1. +/. &* ,*/. ,*/. +00 '* ,*/3 ,*/3 +-(* ,*/, ,*/, +0+ )* ,*/3 ,*/3 +-!+ ,*1/ ,*1/ +1, #+ ,*/,*/+-2 &+ ,*21 ,*21 +0/ '+ ,*/. ,*/. +0) (+ ,*/+ ,*/+ +0) )+ ,*/2 ,*/2 +-+ #,-./01$,2314

PAGE 88

! 76 lanes available to trucks is two, which is constant across the brid ge giving the average daily truck traffic in a single lane, (ADTT) SL of 1,011 trucks. The ends of the partial cover plates are located 15 feet from the support, which is 16% of the total span length. In order to consider the location near the support, the distance away from the support should be 1/10 (or 10%) of the span length ( AASHTO 20 12), which will affect the number of stress cycles per truck passage. As the end of the partial length cover plate is located within 16% of the span length the detail being analyzed is not close enough to be considered close to the support and an n of 1. 0 will be used in determining fatigue life. As discussed in section 5. 3.4 the girder used in the 95' span regions is a W36x182, with a flange thickness of 1.18 inches which places the girders in detail category E' for determining the fatigue life at the ends of the partial length cover plates ( AASHTO 2012, pg. 6 37). Detail category E' has a fatigue threshold, ( F) th of 2.6 ksi, and a detail category constant, A of 3.9x10 8 ksi 3 Due to the girders being category E' the resistance factor, R R is 1.0, 1.6, and 2.5, for the minimum, evaluation, and mean fatigue life respectively. Transducers were only placed on the first and second spans of the 80' girder spans, and none were placed on the 95' girder spans. From the actual data the effective stress ( f ) eff for the 80' span was at most 60% of that calculated by the using the moments produced by the modeling software Assuming the 95' span responds similar to the 80' span, the effective stress for the 95' span was taken as 70% (60% plus a 10% factor of s afety) of the previously calculated effective stress from the modeling software However, u nlike the 80' span girders, the

PAGE 89

! 77 partial load factor, R S is 1.0 for all cases, because the stress ranges are calculated and not from collected field measurements. From the stresses calculated utilizing t he modeling software and LRFD design requirements the largest effective stress was 3.48 ksi a nd located 34 feet into span 3 of the 95' girder, span 6 of overall bridge length. Taking 70% of the previously calculated stress of 3.48 ksi, gives 2.44 ksi. Usin g the new effective stress in equation 7.1 to estimate the fatigue life for the 95' span girder produces a minimum fatigue life of 73 years. The evaluation and mean fatigue l ife estimate is 117 and 183 years respectively. Refer to table 7. 7 for the 95' span fatigue results and Appendix G for more information.

PAGE 90

! 78 Table 7. 7 Calculated Fatigue Life for the 95' Span Girders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

O PMC G < CC> CO< G PG(P Q G(GO CG R$5*$*,1 C(J?HNC? <(M HI F(PC J(G 3KH3L <(M?HN?O J(JG C(PO JGO FJM G>C

PAGE 91

! 79 8 Results 8 .1 Visual Inspection Fatigue Life Design Results Fatigue life calculations presented in chapter 5 show that in the worst case detail the 80' span girder will last 77 year s, and the 95' span will last 63 years based on the mean fatigue life. The present age of the Evans Bridge is 40 years old, as it was built in 1972. Remaining fatigue life is the difference of the calculated fatigue life less the current age of the member since the calculated fatigue life de termines the life of the member from time of construction Table s 8.1 and 8.2 show the remaining fatigue life of the girders based on the overall fatigue life and current age of the bridge. The minimum the 80' span girder will last is another 37 years an d the minimum the 95 span will last is an additional 23 years from the current year of 2012 based on the mean fatigue life

PAGE 92

! 80 Table 8 1 Estimated Remaining Design Fatigue Life for 80' Span Table 8 2 Estimated Remaining Design Fatigue Life for 95' Span 8.2 Strain Transducer Fatigue Life Results As mentioned in section 8.2 the remaining fatigue life of the bridge is the calculated fatigue life less the current age of 40 years. From the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

PAGE 93

! 81 results presented in section 7 the fatigue life of the 80' span is 126 years, and the 95 span is 117 years based on evaluation life Tables 8.3 and 8.4 below show the remaining fatigue life of the 80' and 95' span girders. Based on these calculations the 80' span has another 86 years of fati gue life remaining, which is 49 years more than by the visual inspection results in section 8.1. The 95' span has 54 years more than the visual inspection ca lculation at a total of 77 years of fatigue life remaining. Table 8 3 Estimated Remaining Evaluation Fatigue Life for 80' Span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

PAGE 94

! 82 Table 8 4 Estimated Remaining Evaluation Fatigue Life for 95' Span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

PAGE 95

! 83 9 Cost Comparison The fatigue analysis results based off of the visual inspection would require retrofits to extend the gir der life beyond 20 years. R etrofits would be made to all of the partial length cover plates at the bottom flanges of the girders. Each retrofit would cost approximately $5,000 and with 12 girders this would cost $60,000 per location. Both the 80' and 95' 3 span girders have four locations where a bottom cover plate exists totaling approximately $720,000 to retrofit the bo ttom flange cover plates. Additionally, some of the top flange cover plates would need to be retrofitted as well. This would require removing a strip of deck above the girder to gain access to the cover plate. The total retrofit cost was estimated at up wards of $1,000,000 Due to the remaining fatigue life of the girders being based on visual inspection and ultimately the worst case scenario CCD and FHU considered the alternative of hiring BDI to gather actual stress data on the Evans Bridge and recalcu late the remaining fatigue life of the girders In order to avoid retrofitting at this time, the girders need to last a minimum of 20 additional years T he results show that a costly retrofit is not necessary at this time, since the shortest remaining fatigue life span was calculated at 55 years for the 80' span and 33 years for the 95' span assuming minimum fatigue life The cost of hiring BDI to gather this data was $22,000, saving CCD and ultimately the taxpayers, at least $978,000 to com plete the rehabilitation project to the Evans Bridge.

PAGE 96

! 84 10 Conclusions and Future Research 1 0 .1 Conclusion s As discovered in early research, two members of the same material with the same physical properties may have different fatigue lives because the imperfections in the particular members are different. With this variation in fatigue life t he finite fatigue life as determined by AASHTO, both the LRFD and the MBE, is only an estimation of the structural member's longevity The probability that a member will fail is dependent on whether the analysis is fo r design or evaluation purposes, which places the burden of the decision heavily on the engineer. Engineering judgment plays a large role in determining the most likely situation to occur regarding evaluation of fatigue life of an existing structure Many factors have been found to affect the variables of fatigue life and ultimately the decision and engineer needs to make Some are simple, such as the remaining fatigue life is negative or zero, but with no visible cracks it is safe to assume that de termination is incorrect and use a higher probability of failure. Other decisions regarding the most likely case of remaining fatigue life can be difficult, such as whether or not the member will last 8 or 22 years based off of minimum or evaluation lives A major asset to the fatigue analyses was, and continues to be, CCD completing biannual bridge inspections of the Evans Bridge. The fatigue critical details can be monitored for cracking and if cracking

PAGE 97

! 85 occurs then a retrofit would be necessary to re pair the girders before fatigue failure occurs. By collecting field measurements, such as ADTT counts and stress cycles, the results become more accurate and fatigue life is extended which can assist in reducing some of the questionability. An additional benefit for completing an analysis from collected stress cycles is the amount of money saved by CCD for the taxpayers. C ompleting analyses based on both a visual inspection and the measured str ess cycles the concluding outcome is that the data gathered by the strain gauges produces less conservative and more realistic results. 10.2 Future Research Much can be done to further the research presented in this thesis, and given the subjectivity to estimating fatigue life, it should. Further investigati ons on ways to reduce weld stress at fatigue critical details would do well to be research ed further, and could be beneficial to a global audience. Additional r esearch pertaining directly to the Evans Bridge should include continuing to collect strain data once the rehabilitation project is complete. If long term strain gauges were installed and monitored from the resurfacing through the next cycle of deterioration, assessments of how the road conditions effect the stress of the bridge could be beneficial for CCD to use in maintaining the bridges across Denver. Another research method which would be of local value, could be to periodically collect traffic and strain data and reanalyze the bridge to determine increa ses in traffi c, increase in truck loading, and contin uing to

PAGE 98

! 86 estimat e the remaining fatigue life of the Evans Bridge This information can be used to help determine what changes are occurring in the estimation and why. Another important topic to research would be the redundancy of the steel girders. If one girder failed, or multiple damaged, would the bridge have total failure? Several 3 span continuous steel girder bridges, such as the Lafayette Street Bridge in Minneapolis St. Paul, the Ontario 35 Brid ge, and I 79 Bridge over the Ohio River, have survived total collapse after the failure of one of the central span girders ( Frangopol and Curley, 1987 ). A study was done on a continuous 3 span steel girder bridge built in the late 196 0's in Weathersfield, VT This study compared field collected strain data to a finite element analysis of the girders following damage to three of the five girders due to an over height truck impact ( Bre–a et al., 2012 ). The three damaged girders had not failed completely an d were able to carry a reduced load. Due to the redundancy of the gi rder system along with unintended composite action with the concrete deck, it was determined that the damaged bridge was still acceptable to carry the highway loads ( Bre–a et al., 2012 ). The case of the Evans Bridge is similar to these, in which it is a 3 span continuous steel girder bridge. It is reasonable to assume the redundancy of the 12 girders would support the bridge if one were to fail Studying the effects of losing the use of a girder due to fatigue failure, on the Evans Bridge, using a finite element analysis would be a good topi c to further investigate for CCD in order to avoid total collapse of the structure.

PAGE 99

! 87 F uture research needs to continue and be expanded especially due to the variability of the subject and lack of research. Denver could be on the forefront of developing these methodologies. By continuing research Denver could help other municipalities across the nation implement practices to be more accurate and save money when analyzing aging structures f or fatigue life

PAGE 100

! 88 REFERENCES Alampalli, S. & Lund, R. (2006). Estimating Fatigue Life of Bridge Components Using Measured Strains Journal of Bridge Engineering 11 (6), 725 736. American Association of State Highway and Transportaion Officials. (2011). The Manual for Bridge Evaluation. (2nd ed.) Washington, DC: American Association of State Highway and Transportation Officials. American Association of State Highway and Transportaion Officials. (2012). AASHTO LRFD Bridge Design Specifications. (6 th ed.) Washington, DC: American Association of State Highway and Transportation Officials. Bowman, M., Fu, G., Zhou, Y. E., Connor, R. & Godbole, A. National Coopertive Highway Research Program. (2012). NCHRP Report 721 Fatigue Evaluation of Steel Bridges. Washington, DC: National Cooperative Highway Research Program. Bre–a, S., Jeffery, A. & Civjan, S. (2012, April 10). Evaluation of a Non composite Steel Girder Bridge through Live load Field Testing Journal of Bridge Engineering 1 19. Bridge Diagnostics Inc., (2011). 5.2 BDI Strain Transducer ST350 Boulder, CO: Unpublished. Retrieved from http://bridgetest.com/products/bdi strain transducers/ Chotickai, P. & Bowman, M. (2006). Com parative Study of Fatigue Provisions for the AASHTO Fatigue Guide Specifications and LRFR Manual for Evaluation Journal of Bridge Engineering 11 (5), 655 660. Desai, J. (2007, October 29). Usin a Strain Gauge Transduer in a Wheatstone Bridge Configuration, When Deploying this Classic, Versitaile Circuit Configuration to Measure Strain, Include a Dummy Gauge for Best Results Electronic Engineering Times. CMP Media, Inc., 29 Oct. 2007. Retrieved from http://www.eetimes.com/design/analog design/4009984/Using a strain gauge transducer in a Wheatstone bridge configuration Connor, R., Dexter, R. & H. National Coo pertive Highway Research Program. (2005). NCHRP Synthesis 354 Inspection and Management of Bridges with Fracture Critical Details Washington, DC: National Cooperative Highway Research Program.

PAGE 101

! 89 Fe deral Highway Administration (n.d.). Questions and Answers on the National Bridge Inspection Standards 23 CFR 650 subpart C Bridge Technology. n.d Retrieved October 3, 2012 from http://www.fhwa.dot.gov/bridge/nbis/ Felsburg, Holt, & Ullevig, & LONCO, City and County of Denver. (2011, August ). West Evans Avenue Bridge Condition Inspection Report Addendum 1 Additional Fatigue Tesing and Evaluation. Unpublished. Frangopol, D. & Curley, J. (1987, July ). Effects of Damage and Redundancy on Struc tural Reliability Journal of Structural Engineering 113 (7), 1533 1549. Frost, N. E., Marsh, K. J. & Pook, L. P. (1974). Metal Fatigue Oxford, England: Clarendon Press. Ghahremani, K. & Walbridge, S. (2011). Fatigue Testing and Analysis of Peened Highwa y Bridge Under In Service Variable Amplitude Loading Conditions International Journal of Fatigue 33 300 312. Hawkins, K. P. City and County of Denver. (1996, August 8). Column Analysis West Evans Avenue over Santa Fe Drive. Unpublished. Howell, D. & Shenton, H. (2006). System for In Service Strain Monitoring of Ordinary Bridges Journal of Bridge Engineering 11 (6), 673 680. Kwon, K. & Frangopol, D. (2010). Bridge Fatigue Reliability Assessment Using Probability Density Functions of Equivalent Stress Range Based on Field Monitoring Data International Journal of Fatigue 32 1221 1232. Li, C. City and County of Denver. (2000, May ). West Evans Avenue Bridge Over South Santa Fe Drive Bearing Field Inspection Report Unpublished. Li, C. City and County of Denver. (2001, September ). West Avenue Bridge Over South Santa Fe Drive Movement and Stress Study Report Unpublished. LONCO, City and County of Denver. (1994, December 2). 1994 Inspection of Structure No. D 03 V 180. Unpublished. LONCO, City and County of Denver. (1996, October 10). 1996 Inspection of Structure No. D 03 V 180. Unpublished. LONCO, City and County of Denver. (1997, October 22). 1997 Inspection of Structure No. D 03 V 108. Unpublished. LONCO, City and County of Denver. (1998, Decem ber 29). 1998 Inspection of Structure No. D 03 V 108. Unpublished.

PAGE 102

! 90 LONCO, City and County of Denver. (2000, September 15). 2000 Inspection of Structure No. D 03 V 108. Unpublished. LONCO, City and County of Denver. (2002, October 3). 2002 Inspection of S tructure No. D 03 V 108. Unpublished. LONCO, City and County of Denver. (2004, August 30). 2004 Inspection of Structure No. D 03 V 108. Unpublished. LONCO, City and County of Denver. (2006, October 16). 2006 Inspection of Structure No. D 03 V 108. Unpubl ished. Pook, L. (1983). The Role of Crack Growth in Metal Fatigue Bristol, England: J.W. Arrowsmith Ltd. Pook, L. (2007). Metal Fatigue: What It It, Why It Matters Dordrecht, Netherlands: Springer. Poutiainen, I. & Marquis, G. (2006). A Fatigue Assessment Method Based on Weld Stress International Journal of Fatigue 28 1037 046. Rens, K. L. & Transue, D. J. (2002, July/August ). Tomographic Imaging of Cracked Pier Cap of Evans over Santa Fe Bridge Concrete Repair Bulletin 12 15. Schijve, J. (2 009). Fatigue of Structures and Materials (2nd ed. ) Dordrecht, Netherlands: Springer Science+Business Media. Short Elliott Hendrickson Inc., City and County of Denver. (2008, October 23). 2008 Bridge Inspection Report of Structure No. D 03 V 108. Unpublished. Short Elliott Hendrickson Inc., City and County of Denver. (2010, November 4). 2010 Bridge Inspection Report of Structure No. D 03 V 108. Unpublished. Spangenburg, L. (1876). The Fatigue of Metals Under Repeated Strains New York: Van Nost rand. Stefanescu, D. M. (2011). Handbook of Force Transducers Principles and Componenets Springer Verlag Berlin Heidelberg. Zhao, Z. & Haldar, A. (1994, May ). Fatigue Reliability Evaluation of Steel Bridges Journal of Structural Engineering 120 (5), 1608 1623.

PAGE 103

! 91 Zhao, Z. & Haldar, A. (1996). Bridge Fatigue Damage Evaluation and Updating Using Non Destructive Inspections Engineering Fracture Mechanics 53 (5), 775 788. Zhou, Y. E. (2006). Assessment of Bridge Remaining Fatigue Life through Field Strai n Measurement Journal of Bridge Engineering 11 (6), 737 744.

PAGE 104

! 92 APPENDIX A 80' Span Girder Section Properties

PAGE 105

! 93 #$%&' () *+%,-.&/0#!0-100!0.4#/0&-056%&0, 78-0,9 :;#-<0#+%,-.&/0#=584#-<0#23!0.4#4%+#>8%&-#-8#-<0#4%+>8%&-#8=#?%@0ម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

PAGE 106

! 94 APPENDIX B 95' Span Girder Section Properties

PAGE 107

! 95 #$%&' () *+%,-.&/0#!0-100!0.4#/0&-056%&0, & 7 89-0,: ;<#-=0#+%,-.&/0#>594#-=0#23!0.4#4%+#?9%&-#-9#-=0#4%+?9%&-#9>#@%A0ម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
PAGE 108

! 96 APPENDIX C 80' Span Girder Fatigue Analysis

PAGE 109

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

PAGE 110

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

PAGE 111

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

PAGE 112

! 100 APPENDIX D 95' Span Girder Fatigue Analysis

PAGE 113

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k f t ( ) 1 2 i n f t ( ) i n 3 = k s i

PAGE 114

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n ( A D T T ) S L [ ( f ) e f f ] 3

PAGE 115

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

PAGE 116

! 104 APPENDIX E ADTT Counts

PAGE 117

! 105 Combined File Name: Untitled Axle Classification Start Date: 3/8/2011 ADTT = 1,522 Trucks Start Time: 5:00:00 PM Site Code: 1 Station ID: Location 1: EB Evans Location 2: West of Santa Fe Interchange PWTES Bikes Cars & Trailer 2 Axle Long Buses 2 Axle 6 Tire 3 Axle Single 4 Axle Single <5 Axle Single 5 Axle Double >6 Axle Double <6Axle Multi 6 Axle Multi >6 Axle Multi Not Classified Total Truck Total 3/8/2011 05:00 PM 5 725 155 2 31 4 2 13 3 3 0 3 2 59 1,007 63 3/8/2011 06:00 PM 3 545 124 7 11 1 0 12 0 3 0 0 0 18 724 34 3/8/2011 07:00 PM 4 334 88 4 13 0 0 6 3 0 0 0 0 6 458 26 3/8/2011 08:00 PM 2 292 67 2 6 2 0 2 3 0 0 0 2 7 385 17 3/8/2011 09:00 PM 0 269 50 2 5 0 0 2 4 0 0 0 0 1 333 13 3/8/2011 10:00 PM 0 174 27 1 6 2 0 0 2 0 0 0 0 5 217 11 3/8/2011 11:00 PM 0 107 13 4 3 1 0 0 2 0 0 0 0 0 130 10 Total 14 2446 524 22 75 10 2 35 17 6 0 3 4 96 3,254 174 Percent 0.4% 75.2% 16.1% 0.7% 2.3% 0.3% 0.1% 1.1% 0.5% 0.2% 0.0% 0.1% 0.1% 3.0% 5.3% 3/9/2011 12:00 AM 0 48 12 2 0 0 0 0 5 0 0 0 0 0 67 7 3/9/2011 01:00 AM 0 48 5 4 4 0 0 0 0 0 0 0 0 0 61 8 3/9/2011 02:00 AM 0 45 5 0 2 0 0 0 1 0 0 0 0 0 53 3 3/9/2011 03:00 AM 0 52 5 2 0 0 0 0 2 0 0 0 0 0 61 4 3/9/2011 04:00 AM 0 67 36 11 8 1 0 0 0 0 0 0 0 0 123 20 3/9/2011 05:00 AM 0 239 73 16 18 1 0 4 2 0 0 0 0 8 361 41 3/9/2011 06:00 AM 11 529 145 17 49 5 0 13 10 1 1 0 0 40 821 96 3/9/2011 07:00 AM 10 778 203 14 51 5 1 35 4 6 1 1 0 108 1,217 118 3/9/2011 08:00 AM 5 644 202 14 62 13 2 28 11 3 1 0 2 102 1,089 136 3/9/2011 09:00 AM 14 564 195 7 46 15 1 17 8 2 1 1 0 58 929 98 3/9/2011 10:00 AM 7 518 201 18 65 11 0 22 5 3 0 0 0 36 886 124 3/9/2011 11:00 AM 7 595 194 14 61 10 0 21 17 0 1 0 2 47 969 126 3/9/2011 12:00 PM 6 682 216 10 51 9 0 26 5 2 1 1 1 39 1,049 106 3/9/2011 01:00 PM 10 593 201 13 39 10 1 32 7 2 1 0 1 84 994 106 3/9/2011 02:00 PM 3 687 197 17 50 8 0 23 5 0 1 0 0 42 1,033 104 3/9/2011 03:00 PM 9 685 171 9 42 9 1 8 2 1 2 0 1 139 1,079 75 3/9/2011 04:00 PM 9 762 177 8 40 8 0 25 0 3 1 1 1 89 1,124 87 3/9/2011 05:00 PM 6 804 142 6 26 3 1 15 4 1 2 0 3 59 1,072 61 3/9/2011 06:00 PM 3 653 133 9 23 1 0 10 2 2 0 0 0 28 864 47 3/9/2011 07:00 PM 1 387 80 2 4 0 0 7 0 1 0 0 0 7 489 14 3/9/2011 08:00 PM 3 336 53 3 8 0 0 2 2 1 0 0 0 8 416 16 3/9/2011 09:00 PM 0 285 59 2 8 0 0 0 1 0 0 0 0 0 355 11 3/9/2011 10:00 PM 0 186 35 6 2 1 0 2 0 0 0 0 0 1 233 11 3/9/2011 11:00 PM 1 104 13 3 3 0 0 0 7 0 0 0 0 1 132 13 Total 105 10291 2753 207 662 110 7 290 100 28 13 4 11 896 15,477 1432 Percent 0.7% 66.5% 17.8% 1.3% 4.3% 0.7% 0.0% 1.9% 0.6% 0.2% 0.1% 0.0% 0.1% 5.8% 9.3% 3/10/2011 12:00 AM 0 60 10 0 3 1 0 0 2 0 0 0 0 1 77 6 3/10/2011 01:00 AM 0 51 10 7 3 0 0 0 1 0 0 0 0 0 72 11 3/10/2011 02:00 AM 0 57 13 0 3 0 0 0 3 0 0 0 0 0 76 6 3/10/2011 03:00 AM 0 46 16 2 2 0 0 0 3 0 0 0 0 0 69 7 3/10/2011 04:00 AM 0 65 33 9 5 0 0 2 0 0 0 0 0 0 114 16 3/10/2011 05:00 AM 0 224 77 16 22 0 0 2 1 0 0 0 0 6 348 41 3/10/2011 06:00 AM 9 514 163 14 41 5 1 16 8 0 0 0 0 36 807 85 3/10/2011 07:00 AM 16 848 203 16 59 13 2 29 3 4 1 1 2 103 1,300 130 3/10/2011 08:00 AM 7 692 210 16 61 9 2 28 5 4 6 1 2 104 1,147 134 3/10/2011 09:00 AM 5 571 200 12 62 7 0 27 10 2 1 1 1 70 969 123 3/10/2011 10:00 AM 9 555 204 9 49 5 0 16 1 2 0 0 1 55 906 83 3/10/2011 11:00 AM 10 583 220 12 69 4 0 21 14 3 1 1 2 32 972 127 3/10/2011 12:00 PM 15 703 190 12 55 5 0 28 11 1 2 1 0 55 1,078 115 3/10/2011 01:00 PM 15 642 177 11 65 6 1 22 6 5 1 2 1 59 1,013 120 3/10/2011 02:00 PM 13 676 181 21 50 11 0 13 9 1 4 0 0 79 1,058 109 3/10/2011 03:00 PM 6 687 163 6 48 7 0 21 2 0 1 0 1 97 1,039 86 3/10/2011 04:00 PM 11 781 172 10 31 3 0 27 3 5 2 2 0 77 1,124 83 3/10/2011 05:00 PM 14 765 157 7 27 4 0 18 0 2 1 1 1 60 1,057 61 3/10/2011 06:00 PM 5 609 133 9 24 0 0 13 3 3 0 0 1 27 827 53 3/10/2011 07:00 PM 5 449 82 3 13 1 0 5 0 0 0 0 0 11 569 22 3/10/2011 08:00 PM 1 321 67 2 8 0 0 2 2 0 0 0 0 3 406 14 3/10/2011 09:00 PM 1 287 43 2 13 0 0 4 4 0 0 0 0 7 361 23 3/10/2011 10:00 PM 0 228 50 3 5 1 0 1 1 0 0 0 0 2 291 11 3/10/2011 11:00 PM 1 131 11 2 4 0 0 0 3 0 0 0 0 0 152 9 Total 143 10545 2785 201 722 82 6 295 95 32 20 10 12 884 15,832 1475 Percent 0.9% 66.6% 17.6% 1.3% 4.6% 0.5% 0.0% 1.9% 0.6% 0.2% 0.1% 0.1% 0.1% 5.6% 9.3% 3/11/2011 12:00 AM 0 77 15 1 1 0 0 0 1 0 0 0 0 0 95 3 3/11/2011 01:00 AM 0 58 8 0 1 0 0 0 2 0 0 0 0 0 69 3 3/11/2011 02:00 AM 1 75 17 0 6 0 0 0 0 0 0 0 0 0 99 6 3/11/2011 03:00 AM 0 60 9 2 2 1 0 0 1 0 0 0 0 1 76 6 3/11/2011 04:00 AM 1 71 32 9 4 0 0 0 2 0 0 0 0 0 119 15 3/11/2011 05:00 AM 3 190 81 17 25 2 0 4 1 0 0 0 0 5 328 49 3/11/2011 06:00 AM 6 488 147 13 39 9 1 13 5 2 0 0 3 36 762 85 3/11/2011 07:00 AM 19 701 176 17 62 4 1 43 3 5 1 1 3 124 1,160 140 3/11/2011 08:00 AM 8 617 193 14 60 4 1 33 4 5 4 3 0 74 1,020 128 3/11/2011 09:00 AM 5 569 209 9 68 5 1 24 7 0 1 1 1 66 966 117 3/11/2011 10:00 AM 5 574 178 11 66 6 0 18 7 2 0 0 1 43 911 111 3/11/2011 11:00 AM 15 609 200 7 71 6 0 22 7 0 0 2 2 59 1,000 117 3/11/2011 12:00 PM 17 665 186 13 62 8 2 22 10 1 1 0 2 73 1,062 121 3/11/2011 01:00 PM 15 686 185 10 58 5 1 27 11 3 1 1 2 43 1,048 119 3/11/2011 02:00 PM 13 653 188 17 65 6 0 12 6 0 1 1 1 95 1,058 109 3/11/2011 03:00 PM 19 758 199 14 53 4 0 21 2 3 1 0 0 97 1,171 98 3/11/2011 04:00 PM 9 790 188 9 38 4 0 18 1 4 2 0 1 70 1,134 77 3/11/2011 05:00 PM 7 783 147 6 29 5 1 17 1 3 0 0 0 40 1,039 62 3/11/2011 06:00 PM 7 666 154 9 12 1 2 12 2 4 0 0 0 28 897 42 3/11/2011 07:00 PM 2 504 102 4 12 0 0 3 2 2 0 0 0 11 642 23 3/11/2011 08:00 PM 4 360 61 4 8 0 0 5 0 0 0 0 0 6 448 17 3/11/2011 09:00 PM 0 309 50 3 5 1 0 0 2 0 0 0 0 4 374 11 3/11/2011 10:00 PM 0 255 42 3 4 0 0 4 1 0 0 0 0 2 311 12 3/11/2011 11:00 PM 1 180 28 2 2 1 0 1 3 0 0 0 0 2 220 9 Total 157 10698 2795 194 753 72 10 299 81 34 12 9 16 879 16,009 1480 Percent 1.0% 66.8% 17.5% 1.2% 4.7% 0.4% 0.1% 1.9% 0.5% 0.2% 0.1% 0.1% 0.1% 5.5% 9.2% 3/12/2011 12:00 AM 0 130 25 2 4 0 0 0 3 0 0 0 0 0 164 9 3/12/2011 01:00 AM 0 103 20 3 4 0 0 0 2 0 0 0 0 0 132 9 3/12/2011 02:00 AM 0 100 25 0 1 0 0 0 2 0 0 0 0 4 132 3 3/12/2011 03:00 AM 0 82 14 0 4 0 0 0 1 0 0 0 0 0 101 5 3/12/2011 04:00 AM 0 63 22 3 2 0 0 0 0 0 0 0 0 0 90 5 3/12/2011 05:00 AM 1 89 30 8 2 0 0 1 2 0 0 0 0 3 136 13 3/12/2011 06:00 AM 4 213 88 3 12 2 0 2 2 0 1 0 0 4 331 22 3/12/2011 07:00 AM 4 296 117 7 29 3 0 7 2 0 0 0 0 6 471 48 3/12/2011 08:00 AM 2 473 148 7 46 3 0 14 5 1 1 0 1 27 728 78 3/12/2011 09:00 AM 1 522 167 11 25 4 0 6 3 0 1 0 0 22 762 50 3/12/2011 10:00 AM 4 554 149 6 26 2 1 19 3 2 0 1 0 20 787 60 3/12/2011 11:00 AM 9 563 160 2 43 1 0 17 3 2 1 0 3 34 838 72 3/12/2011 12:00 PM 9 626 173 2 29 5 0 11 6 2 2 0 0 35 900 57 3/12/2011 01:00 PM 11 569 132 1 20 2 0 16 2 0 0 0 0 32 785 41 Wednesday Thursday Friday Saturday Tuesday

PAGE 118

! 106 3/12/2011 02:00 PM 6 650 113 4 29 2 1 7 1 1 1 0 0 17 832 46 3/12/2011 03:00 PM 9 619 123 2 26 2 0 14 0 0 1 1 0 18 815 46 3/12/2011 04:00 PM 10 643 111 2 25 0 0 5 1 0 0 0 1 22 820 34 3/12/2011 05:00 PM 4 512 125 5 21 1 1 5 2 1 0 0 0 14 691 36 3/12/2011 06:00 PM 1 483 111 2 12 0 0 5 0 0 0 0 0 8 622 19 3/12/2011 07:00 PM 3 367 94 2 4 0 0 5 0 0 0 0 0 8 483 11 3/12/2011 08:00 PM 1 297 50 4 7 0 0 2 0 0 0 0 0 3 364 13 3/12/2011 09:00 PM 1 306 63 1 5 0 0 1 0 0 0 0 0 3 380 7 3/12/2011 10:00 PM 0 248 46 3 6 0 0 1 0 0 0 1 0 5 310 11 3/12/2011 11:00 PM 0 202 39 1 4 0 0 0 0 0 0 0 0 4 250 5 Total 80 8710 2145 81 386 27 3 138 40 9 8 3 5 289 11,924 700 Percent 0.7% 73.0% 18.0% 0.7% 3.2% 0.2% 0.0% 1.2% 0.3% 0.1% 0.1% 0.0% 0.0% 2.4% 5.9% 3/13/2011 12:00 AM 1 130 38 1 4 0 0 1 0 0 0 0 0 1 176 6 3/13/2011 01:00 AM 1 130 24 2 3 1 0 1 0 0 0 0 0 2 164 7 3/13/2011 02:00 AM 0 139 26 1 3 0 0 1 1 0 0 0 0 0 171 6 3/13/2011 03:00 AM 0 89 12 4 4 1 0 1 0 0 0 0 0 1 112 10 3/13/2011 04:00 AM 0 72 23 2 4 0 0 1 0 0 0 0 0 0 102 7 3/13/2011 05:00 AM 0 123 32 3 3 0 0 1 0 0 1 0 0 0 163 8 3/13/2011 06:00 AM 0 121 29 6 8 0 0 0 0 0 0 0 0 4 168 14 3/13/2011 07:00 AM 1 205 61 4 10 0 0 0 0 0 0 0 0 4 285 14 3/13/2011 08:00 AM 1 300 69 3 11 0 0 3 0 0 0 0 0 9 396 17 3/13/2011 09:00 AM 0 379 90 1 12 1 0 8 1 0 0 0 0 9 501 23 3/13/2011 10:00 AM 2 398 106 3 19 0 0 7 0 0 1 1 0 15 552 31 3/13/2011 11:00 AM 2 505 107 2 18 1 0 3 2 0 0 0 0 8 648 26 3/13/2011 12:00 PM 4 491 125 2 13 3 0 5 0 1 0 0 0 12 656 24 3/13/2011 01:00 PM 6 562 103 1 19 1 0 8 0 2 0 0 0 14 716 31 3/13/2011 02:00 PM 6 509 128 1 15 0 0 7 0 1 0 0 1 13 681 25 3/13/2011 03:00 PM 15 513 114 1 16 1 0 7 1 1 0 0 1 20 690 28 3/13/2011 04:00 PM 3 527 121 4 17 0 0 7 1 0 0 0 0 16 696 29 3/13/2011 05:00 PM 5 436 98 2 15 1 0 4 0 0 0 0 0 10 571 22 3/13/2011 06:00 PM 2 366 80 3 9 0 1 6 0 0 0 0 0 5 472 19 3/13/2011 07:00 PM 2 340 60 1 7 0 0 1 0 1 0 0 0 2 414 10 3/13/2011 08:00 PM 0 269 56 3 2 1 0 0 0 0 0 0 0 0 331 6 3/13/2011 09:00 PM 0 204 32 0 4 1 0 6 1 0 0 0 0 2 250 12 3/13/2011 10:00 PM 2 123 16 3 4 0 0 0 0 0 0 0 0 1 149 7 3/13/2011 11:00 PM 0 77 13 1 1 0 0 0 1 0 0 0 0 0 93 3 Total 53 7008 1563 54 221 12 1 78 8 6 2 1 2 148 9,157 385 Percent 0.6% 76.5% 17.1% 0.6% 2.4% 0.1% 0.0% 0.9% 0.1% 0.1% 0.0% 0.0% 0.0% 1.6% 4.2% 3/14/2011 12:00 AM 0 48 13 0 2 0 0 0 0 0 0 0 0 0 63 2 3/14/2011 01:00 AM 0 45 8 1 3 0 0 1 0 0 0 0 0 0 58 5 3/14/2011 02:00 AM 0 41 5 1 1 0 0 0 0 0 0 0 0 1 49 2 3/14/2011 03:00 AM 0 55 26 10 3 0 0 1 1 0 0 0 0 0 96 15 3/14/2011 04:00 AM 1 165 54 18 20 2 0 4 0 0 0 0 0 2 266 44 3/14/2011 05:00 AM 4 454 132 16 33 3 0 16 4 2 0 0 3 28 695 77 3/14/2011 06:00 AM 5 664 156 19 51 4 0 18 5 1 1 1 2 54 981 102 3/14/2011 07:00 AM 6 648 182 16 62 4 2 36 6 1 0 1 0 107 1,071 128 3/14/2011 08:00 AM 8 543 188 10 54 13 0 29 6 1 1 1 0 52 906 115 3/14/2011 09:00 AM 12 461 219 7 74 8 0 13 13 1 0 2 0 60 870 118 3/14/2011 10:00 AM 3 532 214 9 71 11 0 17 7 2 2 2 0 39 909 121 3/14/2011 11:00 AM 9 583 198 12 56 9 0 25 8 1 2 0 1 56 960 114 3/14/2011 12:00 PM 6 623 200 9 64 8 0 19 7 1 0 1 0 53 991 109 3/14/2011 01:00 PM 18 623 176 15 47 7 2 17 2 0 1 0 2 93 1,003 93 3/14/2011 02:00 PM 10 724 173 13 49 7 0 30 3 4 0 0 1 100 1,114 107 3/14/2011 03:00 PM 8 776 184 10 41 1 1 19 1 1 1 0 1 87 1,131 76 3/14/2011 04:00 PM 8 750 158 6 34 3 1 17 0 1 1 0 1 57 1,037 64 3/14/2011 05:00 PM 8 575 131 7 24 5 0 11 1 1 0 0 0 25 788 49 3/14/2011 06:00 PM 4 425 123 5 15 0 0 4 1 0 0 0 0 11 588 25 3/14/2011 07:00 PM 6 344 63 2 10 0 0 2 2 0 0 0 0 4 433 16 3/14/2011 08:00 PM 1 282 57 2 5 0 1 4 2 0 0 0 0 4 358 14 3/14/2011 09:00 PM 0 194 32 3 3 0 0 1 1 0 0 0 0 1 235 8 3/14/2011 10:00 PM 1 115 16 2 4 2 0 0 4 0 0 0 0 1 145 12 3/14/2011 11:00 PM 0 56 19 2 2 1 0 0 3 0 0 0 0 1 84 8 Total 118 9726 2727 195 728 88 7 284 77 17 9 8 11 836 14,831 1424 Percent 0.8% 65.6% 18.4% 1.3% 4.9% 0.6% 0.0% 1.9% 0.5% 0.1% 0.1% 0.1% 0.1% 5.6% 9.6% 3/15/2011 12:00 AM 0 33 16 2 1 2 0 1 4 0 0 0 0 0 59 10 3/15/2011 01:00 AM 0 49 13 0 4 1 0 1 1 0 0 0 0 1 70 7 3/15/2011 02:00 AM 0 45 8 1 2 0 0 1 1 0 0 0 0 0 58 5 3/15/2011 03:00 AM 0 58 34 8 5 0 0 1 3 0 0 0 0 2 111 17 3/15/2011 04:00 AM 1 172 50 17 16 1 0 1 1 0 0 0 1 4 264 37 3/15/2011 05:00 AM 6 460 130 17 36 5 0 15 8 4 0 0 1 19 701 86 3/15/2011 06:00 AM 18 714 176 17 50 7 0 31 3 4 2 3 3 108 1,136 120 3/15/2011 07:00 AM 15 648 218 17 66 9 1 32 10 7 0 4 1 95 1,123 147 3/15/2011 08:00 AM 8 582 202 10 72 5 0 24 11 2 1 1 4 62 984 130 3/15/2011 09:00 AM 6 551 202 8 43 9 0 27 9 0 0 2 0 49 906 98 3/15/2011 10:00 AM 2 571 215 14 65 8 0 33 7 2 0 0 2 37 956 131 3/15/2011 11:00 AM 13 621 205 15 63 5 0 23 9 4 2 0 0 46 1,006 121 3/15/2011 12:00 PM 4 635 217 6 61 3 1 24 7 2 0 3 1 49 1,013 108 3/15/2011 01:00 PM 12 605 202 26 47 9 0 19 3 2 1 1 0 73 1,000 108 3/15/2011 02:00 PM 9 697 164 13 48 7 1 33 3 6 0 1 0 103 1,085 112 3/15/2011 03:00 PM 14 747 190 14 37 4 1 21 1 1 1 1 0 80 1,112 81 3/15/2011 04:00 PM 8 743 138 4 34 2 0 17 4 2 1 0 0 57 1,010 64 3/15/2011 05:00 PM 5 601 132 7 28 1 0 12 2 0 0 0 0 37 825 50 3/15/2011 06:00 PM 6 432 99 7 17 1 0 10 5 3 0 0 0 7 587 43 3/15/2011 07:00 PM 0 341 63 6 5 1 0 2 1 0 0 0 0 9 428 15 3/15/2011 08:00 PM 1 300 44 1 7 1 0 5 1 0 0 0 0 3 363 15 3/15/2011 09:00 PM 1 172 34 3 3 0 0 0 2 1 0 0 0 2 218 9 3/15/2011 10:00 PM 0 115 28 2 2 1 0 1 3 0 0 0 0 0 152 9 3/15/2011 11:00 PM 0 73 23 1 0 2 0 0 9 0 0 0 0 1 109 12 Total 129 9965 2803 216 712 84 4 334 108 40 8 16 13 844 15,276 1535 Percent 0.8% 65.2% 18.3% 1.4% 4.7% 0.5% 0.0% 2.2% 0.7% 0.3% 0.1% 0.1% 0.1% 5.5% 10.0% 3/16/2011 12:00 AM 0 47 12 2 1 0 0 0 3 0 0 0 0 0 65 6 3/16/2011 01:00 AM 0 55 6 0 0 0 0 0 2 0 0 0 0 2 65 2 3/16/2011 02:00 AM 0 43 9 1 3 0 0 1 2 0 0 0 0 0 59 7 3/16/2011 03:00 AM 1 56 35 11 3 0 0 0 0 0 0 0 0 1 107 14 3/16/2011 04:00 AM 0 177 69 12 24 1 0 8 0 0 0 0 0 3 294 45 3/16/2011 05:00 AM 10 447 138 15 29 8 1 12 4 1 1 0 1 35 702 72 3/16/2011 06:00 AM 8 733 174 19 49 7 0 20 6 5 1 0 4 115 1,141 111 3/16/2011 07:00 AM 10 680 198 13 93 7 1 33 8 5 4 0 4 100 1,156 168 3/16/2011 08:00 AM 3 596 190 17 57 10 0 29 14 4 2 0 3 41 966 136 3/16/2011 09:00 AM 10 508 199 15 43 10 0 28 14 3 0 0 3 41 874 116 3/16/2011 10:00 AM 13 511 206 11 62 12 0 17 12 0 1 1 1 59 906 117 3/16/2011 11:00 AM 13 584 209 12 64 8 0 27 7 3 0 0 1 56 984 122 3/16/2011 12:00 PM 10 620 193 14 56 9 0 18 4 1 1 1 0 57 984 104 3/16/2011 01:00 PM 6 646 193 14 45 6 0 25 8 0 0 0 0 77 1,020 98 3/16/2011 02:00 PM 10 769 159 13 50 3 2 20 7 4 1 1 0 74 1,113 101 3/16/2011 03:00 PM 10 767 178 7 35 3 1 29 4 3 2 1 2 65 1,107 87 3/16/2011 04:00 PM 8 793 133 7 29 2 1 22 6 2 1 0 1 57 1,062 71 3/16/2011 05:00 PM 11 631 126 7 26 2 0 12 2 1 0 1 0 42 861 51 3/16/2011 06:00 PM 9 501 111 4 16 0 0 10 3 0 0 0 0 13 667 33 3/16/2011 07:00 PM 4 353 64 3 6 0 0 5 1 0 0 0 0 10 446 15 3/16/2011 08:00 PM 6 332 57 2 8 2 0 6 1 1 0 0 0 10 425 20 3/16/2011 09:00 PM 0 240 51 2 4 3 0 4 7 0 0 0 0 8 319 20 3/16/2011 10:00 PM 0 136 22 3 1 2 0 0 1 0 0 0 0 1 166 7 3/16/2011 11:00 PM 1 81 11 3 2 3 0 0 5 0 0 0 0 1 107 13 Saturday Sunday Monday Tuesday Wednesday

PAGE 119

! 107 Total 143 10306 2743 207 706 98 6 326 121 33 14 5 20 868 15,596 1536 Percent 0.9% 66.1% 17.6% 1.3% 4.5% 0.6% 0.0% 2.1% 0.8% 0.2% 0.1% 0.0% 0.1% 5.6% 9.8% 3/17/2011 12:00 AM 0 56 5 2 0 2 0 0 1 0 0 0 0 0 66 5 3/17/2011 01:00 AM 0 61 10 0 4 1 0 0 2 0 0 0 0 0 78 7 3/17/2011 02:00 AM 0 48 15 0 2 0 0 2 2 0 0 0 0 1 70 6 3/17/2011 03:00 AM 1 49 25 10 3 0 0 5 4 0 0 0 0 0 97 22 3/17/2011 04:00 AM 1 153 67 14 25 1 0 3 2 0 0 0 0 3 269 45 3/17/2011 05:00 AM 7 472 124 16 37 3 0 14 5 3 0 0 0 26 707 78 3/17/2011 06:00 AM 9 723 177 18 52 4 2 40 7 0 0 0 3 98 1,133 126 3/17/2011 07:00 AM 7 695 207 10 62 7 2 26 8 7 1 0 2 123 1,157 125 3/17/2011 08:00 AM 8 584 212 10 67 11 1 15 9 2 0 0 1 75 995 116 3/17/2011 09:00 AM 6 545 203 9 61 7 0 21 16 1 0 1 1 61 932 117 3/17/2011 10:00 AM 7 615 181 5 58 9 0 22 11 1 0 1 0 49 959 107 3/17/2011 11:00 AM 8 642 188 14 56 7 0 21 10 1 0 1 0 56 1,004 110 3/17/2011 12:00 PM 13 595 173 10 53 10 1 25 6 6 1 0 3 42 938 115 3/17/2011 01:00 PM 10 696 190 16 66 6 0 14 9 2 2 0 1 41 1,053 116 3/17/2011 02:00 PM 20 662 164 10 60 3 2 23 8 2 1 0 1 121 1,077 110 3/17/2011 03:00 PM 9 711 199 11 40 4 0 25 2 4 0 0 3 79 1,087 89 3/17/2011 04:00 PM 8 731 148 6 22 2 0 25 3 3 1 0 0 60 1,009 62 3/17/2011 05:00 PM 5 609 127 5 19 2 0 15 2 2 0 0 0 16 802 45 3/17/2011 06:00 PM 3 503 94 4 13 1 0 4 3 0 0 0 0 13 638 25 3/17/2011 07:00 PM 2 370 62 2 10 1 0 5 1 0 0 0 0 2 455 19 3/17/2011 08:00 PM 3 292 43 3 4 0 0 2 4 0 0 0 0 9 360 13 3/17/2011 09:00 PM 0 267 42 2 10 0 0 0 3 0 0 0 0 3 327 15 3/17/2011 10:00 PM 0 151 32 4 7 1 0 0 2 0 0 0 0 2 199 14 3/17/2011 11:00 PM 1 86 20 3 1 2 0 0 2 0 0 0 0 4 119 8 Total 128 10316 2708 184 732 84 8 307 122 34 6 3 15 884 15,531 1495 Percent 0.8% 66.4% 17.4% 1.2% 4.7% 0.5% 0.1% 2.0% 0.8% 0.2% 0.0% 0.0% 0.1% 5.7% 9.6% 3/18/2011 12:00 AM 0 60 16 2 2 1 0 0 2 0 0 0 0 1 84 7 3/18/2011 01:00 AM 0 83 21 2 3 0 0 1 0 0 0 0 0 1 111 6 3/18/2011 02:00 AM 0 65 17 1 1 1 0 0 2 0 0 0 0 1 88 5 3/18/2011 03:00 AM 0 71 27 8 4 0 0 2 0 0 0 0 0 0 112 14 3/18/2011 04:00 AM 0 162 61 14 19 1 0 4 3 0 0 0 0 6 270 41 3/18/2011 05:00 AM 2 417 97 18 24 5 0 10 4 1 1 0 1 29 609 64 3/18/2011 06:00 AM 9 697 170 24 46 13 1 25 6 2 1 0 3 71 1,068 121 3/18/2011 07:00 AM 7 677 209 11 63 7 0 23 6 5 5 1 0 88 1,102 121 3/18/2011 08:00 AM 7 540 213 8 62 14 0 33 8 0 1 0 1 57 944 127 3/18/2011 09:00 AM 5 514 193 14 65 9 0 26 8 1 0 0 2 34 871 125 3/18/2011 10:00 AM 8 554 206 16 62 10 1 28 8 3 1 0 2 62 961 131 3/18/2011 11:00 AM 3 618 191 10 55 11 0 32 5 5 3 1 1 69 1,004 123 3/18/2011 12:00 PM 8 610 200 11 62 10 0 33 5 3 1 0 0 72 1,015 125 3/18/2011 01:00 PM 5 652 201 17 50 5 0 18 4 4 0 0 0 76 1,032 98 3/18/2011 02:00 PM 7 740 199 12 48 7 0 25 2 6 2 0 2 97 1,147 104 3/18/2011 03:00 PM 8 814 168 6 37 3 1 20 1 1 3 0 0 106 1,168 72 3/18/2011 04:00 PM 7 773 164 5 21 2 0 23 4 3 2 1 0 38 1,043 61 3/18/2011 05:00 PM 5 644 126 7 22 1 0 16 2 0 1 0 1 29 854 50 3/18/2011 06:00 PM 5 542 95 5 13 1 0 12 3 0 0 0 0 13 689 34 3/18/2011 07:00 PM 2 368 88 4 8 2 0 8 3 0 0 0 0 10 493 25 3/18/2011 08:00 PM 0 381 64 3 5 0 1 3 2 0 0 0 0 7 466 14 3/18/2011 09:00 PM 0 327 61 3 4 0 0 0 2 0 1 0 0 5 403 10 3/18/2011 10:00 PM 2 204 22 0 6 1 0 4 1 0 0 0 0 3 243 12 3/18/2011 11:00 PM 1 156 25 2 5 0 0 0 1 0 0 0 0 1 191 8 Total 91 10669 2834 203 687 104 4 346 82 34 22 3 13 876 15,968 1498 Percent 0.6% 66.8% 17.7% 1.3% 4.3% 0.7% 0.0% 2.2% 0.5% 0.2% 0.1% 0.0% 0.1% 5.5% 9.4% 3/19/2011 12:00 AM 0 96 21 3 9 0 0 0 3 0 0 0 0 0 132 15 3/19/2011 01:00 AM 0 130 17 3 3 0 0 1 3 0 0 0 0 0 157 10 3/19/2011 02:00 AM 1 73 15 0 2 0 0 0 1 0 0 0 0 0 92 3 3/19/2011 03:00 AM 0 65 17 2 3 0 0 0 1 0 0 0 0 0 88 6 3/19/2011 04:00 AM 0 80 27 8 3 0 0 1 0 0 0 0 0 0 119 12 3/19/2011 05:00 AM 1 151 55 5 5 1 1 6 2 0 0 0 0 0 227 20 3/19/2011 06:00 AM 0 252 101 5 18 3 0 6 1 1 0 0 0 5 392 34 3/19/2011 07:00 AM 7 398 133 6 29 2 0 6 2 1 0 0 0 15 599 46 3/19/2011 08:00 AM 5 472 144 5 29 6 0 8 5 0 2 0 0 26 702 55 3/19/2011 09:00 AM 5 557 154 5 37 2 0 11 5 1 0 1 0 24 802 62 3/19/2011 10:00 AM 11 613 183 5 39 1 0 8 3 1 1 0 0 28 893 58 3/19/2011 11:00 AM 8 673 160 8 42 1 0 14 4 0 1 1 1 33 946 72 3/19/2011 12:00 PM 12 669 151 3 28 1 0 16 3 1 3 1 0 39 927 56 3/19/2011 01:00 PM 11 629 165 2 29 1 0 16 0 1 2 1 0 32 889 52 3/19/2011 02:00 PM 11 633 140 3 28 2 0 10 0 1 0 0 1 39 868 45 3/19/2011 03:00 PM 4 596 167 4 32 1 1 9 1 0 0 0 0 32 847 48 3/19/2011 04:00 PM 9 593 140 3 28 0 0 9 2 0 0 0 0 23 807 42 3/19/2011 05:00 PM 5 478 121 3 25 0 0 11 0 2 0 0 0 16 661 41 3/19/2011 06:00 PM 2 428 104 5 11 0 0 2 2 0 0 0 0 12 566 20 3/19/2011 07:00 PM 0 384 83 1 5 2 0 0 0 0 0 0 0 9 484 8 3/19/2011 08:00 PM 2 339 62 3 9 0 0 2 0 0 0 0 0 6 423 14 3/19/2011 09:00 PM 1 317 58 3 3 0 0 3 0 0 0 0 0 5 390 9 3/19/2011 10:00 PM 1 243 48 0 6 0 0 1 0 0 1 0 0 2 302 8 3/19/2011 11:00 PM 0 192 25 2 4 1 0 1 0 0 0 0 0 1 226 8 Total 96 9061 2291 87 427 24 2 141 38 9 10 4 2 347 12,539 744 Percent 0.8% 72.3% 18.3% 0.7% 3.4% 0.2% 0.0% 1.1% 0.3% 0.1% 0.1% 0.0% 0.0% 2.8% 5.9% 3/20/2011 12:00 AM 1 112 28 2 1 0 0 1 0 0 0 0 0 1 146 4 3/20/2011 01:00 AM 0 146 22 2 2 0 0 1 0 0 0 0 0 3 176 5 3/20/2011 02:00 AM 0 99 15 0 2 0 0 0 0 0 0 0 0 0 116 2 3/20/2011 03:00 AM 0 83 20 2 3 0 0 0 0 0 0 0 0 0 108 5 3/20/2011 04:00 AM 0 61 14 4 5 0 0 1 1 0 0 0 0 0 86 11 3/20/2011 05:00 AM 0 104 27 2 3 0 0 0 1 0 0 0 0 0 137 6 3/20/2011 06:00 AM 0 131 56 5 10 0 0 0 0 0 0 0 0 0 202 15 3/20/2011 07:00 AM 3 224 61 5 11 1 0 1 0 0 0 0 0 2 308 18 3/20/2011 08:00 AM 2 332 90 2 8 1 1 4 0 1 0 0 0 11 452 17 3/20/2011 09:00 AM 3 424 94 1 12 1 0 7 0 2 0 0 0 9 553 23 3/20/2011 10:00 AM 7 451 105 2 25 1 0 3 0 1 0 0 0 10 605 32 3/20/2011 11:00 AM 7 527 125 2 13 0 0 7 1 0 1 0 0 14 697 24 3/20/2011 12:00 PM 7 492 118 2 16 0 1 11 2 0 0 0 0 12 661 32 3/20/2011 01:00 PM 8 521 107 1 18 2 0 3 0 1 1 0 0 23 685 26 3/20/2011 02:00 PM 13 506 93 2 19 3 1 11 0 1 0 0 0 24 673 37 3/20/2011 03:00 PM 4 543 108 1 19 2 1 1 1 0 0 0 0 17 697 25 3/20/2011 04:00 PM 7 490 109 6 18 2 0 4 0 1 1 0 0 14 652 32 3/20/2011 05:00 PM 4 424 96 3 12 2 0 4 1 0 0 0 0 19 565 22 3/20/2011 06:00 PM 1 349 90 1 8 1 0 3 2 2 0 0 0 9 466 17 3/20/2011 07:00 PM 1 341 68 2 7 1 0 1 1 0 0 0 0 9 431 12 3/20/2011 08:00 PM 1 274 53 3 5 0 0 0 0 0 0 0 0 9 345 8 3/20/2011 09:00 PM 0 198 46 3 6 1 0 0 1 0 0 0 0 1 256 11 3/20/2011 10:00 PM 0 115 27 3 5 1 0 1 1 0 0 0 0 2 155 11 3/20/2011 11:00 PM 0 90 14 0 2 1 0 0 1 0 0 0 0 1 109 4 Total 69 7037 1586 56 230 20 4 64 13 9 3 0 0 190 9,281 399 Percent 0.7% 75.8% 17.1% 0.6% 2.5% 0.2% 0.0% 0.7% 0.1% 0.1% 0.0% 0.0% 0.0% 2.0% 4.3% 3/21/2011 12:00 AM 0 49 14 0 3 0 0 0 1 0 0 0 0 0 67 4 3/21/2011 01:00 AM 0 54 14 0 1 2 0 1 1 0 0 0 0 0 73 5 3/21/2011 02:00 AM 0 41 8 0 2 3 0 0 2 0 0 0 0 0 56 7 3/21/2011 03:00 AM 0 49 27 11 4 1 0 1 0 0 0 0 0 1 94 17 3/21/2011 04:00 AM 0 112 73 14 26 2 0 4 2 0 0 0 0 4 237 48 3/21/2011 05:00 AM 2 367 118 16 24 2 1 11 6 0 0 0 1 43 591 61 Saturday Sunday Monday Thursday Friday

PAGE 120

! 108 3/21/2011 06:00 AM 11 683 160 17 34 9 0 31 5 8 2 0 1 105 1,066 107 3/21/2011 07:00 AM 13 553 214 20 69 12 0 36 6 4 5 0 2 192 1,126 154 3/21/2011 08:00 AM 4 419 177 9 51 11 1 25 9 1 0 0 1 178 886 108 3/21/2011 09:00 AM 6 427 182 13 51 13 0 18 3 2 0 0 0 220 935 100 3/21/2011 10:00 AM 8 427 177 12 64 4 0 20 4 0 1 0 0 262 979 105 3/21/2011 11:00 AM 13 507 163 10 37 7 0 20 6 0 1 0 0 267 1,031 81 3/21/2011 12:00 PM 9 435 187 16 58 5 0 17 3 0 1 1 1 265 998 102 3/21/2011 01:00 PM 5 514 157 14 36 6 0 9 2 1 1 1 1 316 1,063 71 3/21/2011 02:00 PM 7 575 162 8 35 6 0 11 2 0 0 0 0 243 1,049 62 3/21/2011 03:00 PM 3 566 126 9 28 2 0 14 0 0 1 1 0 264 1,014 55 3/21/2011 04:00 PM 4 622 121 4 24 1 0 14 1 0 2 0 0 265 1,058 46 3/21/2011 05:00 PM 7 455 113 7 19 1 0 11 0 0 0 0 0 244 857 38 3/21/2011 06:00 PM 1 344 87 5 9 0 0 1 1 0 0 0 0 153 601 16 3/21/2011 07:00 PM 0 267 56 6 9 0 0 2 1 0 0 0 0 114 455 18 3/21/2011 08:00 PM 4 214 33 2 6 0 0 1 0 0 0 0 0 95 355 9 3/21/2011 09:00 PM 1 166 22 3 4 2 0 1 2 0 0 0 0 87 288 12 3/21/2011 10:00 PM 0 79 16 2 2 0 0 0 0 0 0 0 0 44 143 4 3/21/2011 11:00 PM 1 57 7 1 2 0 0 1 8 0 0 0 0 32 109 12 Total 99 7982 2414 199 598 89 2 249 65 16 14 3 7 3394 15,131 1242 Percent 0.7% 52.8% 16.0% 1.3% 4.0% 0.6% 0.0% 1.6% 0.4% 0.1% 0.1% 0.0% 0.0% 22.4% 8.2% 3/22/2011 12:00 AM 0 49 8 2 1 0 0 0 0 0 0 0 0 15 75 3 3/22/2011 01:00 AM 0 32 10 0 2 0 0 0 0 0 0 0 0 22 66 2 3/22/2011 02:00 AM 0 14 2 0 3 0 0 0 1 0 0 0 0 26 46 4 3/22/2011 03:00 AM 0 31 14 8 0 0 0 1 1 0 0 0 0 31 86 10 3/22/2011 04:00 AM 0 77 37 10 11 0 0 4 2 0 0 0 0 91 232 27 3/22/2011 05:00 AM 6 259 76 14 24 6 0 9 5 1 1 0 0 212 613 60 3/22/2011 06:00 AM 5 492 145 17 29 5 0 30 5 0 1 1 1 298 1,029 89 3/22/2011 07:00 AM 9 527 166 13 62 9 0 20 4 1 0 1 1 306 1,119 111 3/22/2011 08:00 AM 8 457 184 8 54 3 0 18 7 0 1 0 0 283 1,023 91 3/22/2011 09:00 AM 2 391 167 6 43 4 0 13 5 2 1 2 0 272 908 76 3/22/2011 10:00 AM 3 439 143 11 49 2 0 7 7 0 1 1 0 267 930 78 3/22/2011 11:00 AM 9 508 164 6 54 2 0 21 7 0 0 0 1 252 1,024 91 3/22/2011 12:00 PM 6 460 149 5 59 2 0 14 3 1 0 1 0 298 998 85 3/22/2011 01:00 PM 5 477 164 15 48 3 0 14 4 1 3 0 0 281 1,015 88 3/22/2011 02:00 PM 6 560 141 11 35 4 0 14 3 1 1 2 0 302 1,080 71 3/22/2011 03:00 PM 6 618 169 11 41 1 0 21 1 2 2 0 1 276 1,149 80 3/22/2011 04:00 PM 3 608 112 5 16 3 0 17 0 0 1 0 1 275 1,041 43 3/22/2011 05:00 PM 2 475 116 5 19 0 0 7 1 0 1 0 0 266 892 33 3/22/2011 06:00 PM 2 323 78 11 7 0 0 3 0 0 0 0 0 179 603 21 3/22/2011 07:00 PM 0 311 58 3 6 0 0 3 1 0 0 0 0 159 541 13 3/22/2011 08:00 PM 3 194 42 1 7 0 0 0 2 0 0 0 0 115 364 10 3/22/2011 09:00 PM 1 175 34 2 4 1 0 4 5 0 0 0 0 86 312 16 3/22/2011 10:00 PM 0 94 18 2 4 0 0 0 2 0 0 0 0 47 167 8 3/22/2011 11:00 PM 0 45 7 3 5 0 0 0 3 0 0 0 0 37 100 11 Total 76 7616 2204 169 583 45 0 220 69 9 13 8 5 4396 15,413 1121 Percent 0.5% 49.4% 14.3% 1.1% 3.8% 0.3% 0.0% 1.4% 0.4% 0.1% 0.1% 0.1% 0.0% 28.5% 7.3% 3/23/2011 12:00 AM 0 35 5 3 0 0 0 0 0 0 0 0 0 21 64 3 3/23/2011 01:00 AM 0 29 10 0 3 0 0 0 0 0 0 0 0 29 71 3 3/23/2011 02:00 AM 0 14 9 0 3 0 0 0 0 0 0 0 0 18 44 3 3/23/2011 03:00 AM 0 24 12 5 0 0 0 0 1 0 0 0 0 33 75 6 3/23/2011 04:00 AM 1 53 43 12 18 2 0 2 1 1 0 0 0 107 240 36 3/23/2011 05:00 AM 2 253 72 8 16 3 1 9 5 0 0 0 0 244 613 42 3/23/2011 06:00 AM 4 451 148 15 44 5 0 20 5 2 1 0 0 321 1,016 92 3/23/2011 07:00 AM 9 432 164 6 53 7 0 26 4 1 1 1 1 382 1,087 100 3/23/2011 08:00 AM 6 407 157 7 39 3 0 18 6 3 1 1 0 310 958 78 3/23/2011 09:00 AM 4 360 148 6 51 6 0 10 5 0 0 1 0 293 884 79 3/23/2011 10:00 AM 5 425 151 8 47 3 1 19 2 0 1 1 1 313 977 83 3/23/2011 11:00 AM 2 440 170 8 52 5 0 11 5 2 0 0 0 300 995 83 3/23/2011 12:00 PM 5 502 141 8 35 1 0 18 1 0 0 1 0 306 1,018 64 3/23/2011 01:00 PM 5 483 143 11 29 4 1 11 2 1 1 1 0 320 1,012 61 3/23/2011 02:00 PM 7 578 154 12 32 1 0 14 2 1 1 1 1 289 1,093 65 3/23/2011 03:00 PM 5 599 143 10 36 2 0 21 1 0 3 1 2 278 1,101 76 3/23/2011 04:00 PM 4 623 127 5 14 1 0 15 2 2 0 0 0 274 1,067 39 3/23/2011 05:00 PM 5 488 95 6 20 2 0 6 1 0 0 0 0 278 901 35 3/23/2011 06:00 PM 5 354 88 5 10 1 0 4 3 0 0 0 0 198 668 23 3/23/2011 07:00 PM 3 289 52 1 6 0 0 2 2 0 0 0 0 158 513 11 3/23/2011 08:00 PM 0 205 43 1 9 0 0 2 1 0 1 0 0 134 396 14 3/23/2011 09:00 PM 0 175 31 1 3 0 0 0 3 0 0 0 0 125 338 7 3/23/2011 10:00 PM 0 90 16 2 4 2 0 0 4 0 0 0 0 57 175 12 3/23/2011 11:00 PM 0 71 13 3 1 1 0 0 1 0 0 0 0 47 137 6 Total 72 7380 2135 143 525 49 3 208 57 13 10 8 5 4835 15,443 1021 Percent 0.5% 47.8% 13.8% 0.9% 3.4% 0.3% 0.0% 1.3% 0.4% 0.1% 0.1% 0.1% 0.0% 31.3% 6.6% 3/24/2011 12:00 AM 0 33 6 1 1 1 0 1 0 0 0 0 0 34 77 4 3/24/2011 01:00 AM 1 21 20 0 4 2 0 0 1 0 0 0 0 33 82 7 3/24/2011 02:00 AM 0 24 5 0 0 1 0 0 1 0 0 0 0 23 54 2 3/24/2011 03:00 AM 0 16 11 6 1 1 0 0 1 0 0 0 0 56 92 9 3/24/2011 04:00 AM 0 66 37 8 8 0 0 0 0 0 0 0 0 100 219 16 3/24/2011 05:00 AM 1 224 78 11 16 3 0 2 0 0 0 0 0 237 572 32 3/24/2011 06:00 AM 7 367 97 13 18 7 0 20 5 3 0 0 1 309 847 67 3/24/2011 07:00 AM 6 401 148 10 71 6 0 25 5 2 2 0 0 359 1,035 121 3/24/2011 08:00 AM 3 435 154 10 44 4 0 15 2 0 1 1 1 331 1,001 78 3/24/2011 09:00 AM 0 377 124 6 39 4 0 9 8 2 0 1 0 309 879 69 3/24/2011 10:00 AM 2 447 157 14 41 1 0 19 5 1 0 0 1 298 986 82 3/24/2011 11:00 AM 10 475 144 8 43 4 0 12 4 2 2 0 0 316 1,020 75 3/24/2011 12:00 PM 5 434 184 10 44 7 0 24 2 0 0 0 0 276 986 87 3/24/2011 01:00 PM 4 450 164 8 47 5 0 10 2 1 1 0 0 313 1,005 74 3/24/2011 02:00 PM 5 505 130 9 42 3 0 23 1 1 1 0 0 263 983 80 3/24/2011 03:00 PM 1 576 150 7 46 4 1 9 2 1 1 0 0 253 1,051 71 3/24/2011 04:00 PM 5 603 131 8 20 2 0 16 0 1 1 1 0 271 1,059 49 3/24/2011 05:00 PM 2 414 100 3 10 0 0 10 1 0 0 0 0 279 819 24 3/24/2011 06:00 PM 1 303 66 3 8 0 0 2 0 0 1 0 0 203 587 14 3/24/2011 07:00 PM 1 276 38 2 7 0 0 0 0 0 0 0 0 162 486 9 3/24/2011 08:00 PM 0 227 36 2 5 0 0 2 0 0 1 0 0 124 397 10 3/24/2011 09:00 PM 1 175 25 1 7 1 0 0 2 0 0 0 0 102 314 11 3/24/2011 10:00 PM 1 101 15 1 5 0 0 3 1 0 0 0 0 81 208 10 3/24/2011 11:00 PM 0 55 10 1 2 1 0 0 3 0 0 0 0 51 123 7 Total 56 7005 2030 142 529 57 1 202 46 14 11 3 3 4783 14,882 1008 Percent 0.4% 47.1% 13.6% 1.0% 3.6% 0.4% 0.0% 1.4% 0.3% 0.1% 0.1% 0.0% 0.0% 32.1% 6.8% 3/25/2011 12:00 AM 0 36 4 0 3 1 0 0 1 0 0 0 0 34 79 5 3/25/2011 01:00 AM 0 55 9 1 1 0 0 0 3 0 0 0 0 36 105 5 3/25/2011 02:00 AM 0 35 4 0 3 0 0 0 1 0 0 0 0 30 73 4 3/25/2011 03:00 AM 0 19 13 4 1 0 0 0 0 0 0 0 0 34 71 5 3/25/2011 04:00 AM 0 36 16 1 6 0 0 0 0 0 0 0 0 50 109 7 3/25/2011 05:00 AM 0 114 37 0 5 0 0 1 5 0 0 0 0 137 299 11 3/25/2011 06:00 AM 2 289 96 7 25 3 0 6 2 0 0 0 1 285 716 44 3/25/2011 07:00 AM 8 430 158 5 53 12 1 16 4 4 1 1 0 371 1,064 97 3/25/2011 08:00 AM 6 408 156 9 61 3 0 12 2 6 1 1 0 364 1,029 95 3/25/2011 09:00 AM 0 38 14 0 3 1 0 0 0 0 0 0 0 41 97 4 3/25/2011 10:00 AM 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Total 16 1460 507 27 161 20 1 35 18 10 2 2 1 1382 3,642 277 Percent 0.4% 40.1% 13.9% 0.7% 4.4% 0.5% 0.0% 1.0% 0.5% 0.3% 0.1% 0.1% 0.0% 37.9% 7.6% Friday Monday Tuesday Wednesday Thursday

PAGE 121

! 109 APPENDIX F 80' Span Girder Strain Gauge Results

PAGE 122

! 110 !"#$!"% !"%$&"# &"#$&"% &"%$'"# '"#$'"% '"%$("# ("#$("% ("%$%"# %"#$%"% %"%$)"# )"#$)"% )"%$*"# *"#$*"% *"%$+"# +"#$+"% +"%$,"# ,"#$,"% ,"%$!#"# !#"#$!#"% !#"%$!!"# -!! .! !""#$%& $%"'% '&(# (&") !$"# '*' *!" )'& '$ %$ %$ !! ! & & & & & & /! )))'%&) #$$)( !!%#& ())* %)(& !"#' *(% )'$ )*" )$& !'% #' $! )% !( ( ) ! /!01 !$(%!!) %&'$( *)%! )%#! $%) ((( )%% "& )& !$ ) ) & & & & & & & & 2! )))"(#( *&'$! #()* (!)" !%"% "&) ()' )(* '! $$ )& !& ) $ % & & & & & & 3! )!!$)"& #&*%! ')%# )!'# !)#' "$' %&( !"( '! *$ (& !$ !& ) & & & & & 4! )$&!"') '&*"* ""'& )&"% "') %"' !#% !)! !*$ !&% %$ !) # ) % & % & & & & 5! )%(&&"" #%%&# ($$# !!&& ()# !"% #$ !$& !%' %% !& % % ) % & & & & & & .& !*!&)"$ %($%" *#"% )!#' #)% (*% !$% %! # % ! & & & & & & & & & /& !"'"&*( %#'"& $"*) %("" "$* %%" %'& !$& %& !% ( ) & & & & & & & & /&01 !*%%)!! !*&"' %)#$ *$# )#' %! ( ( & & & & & & & & & & & & & 2& !"!#&)( (*&'* ")*$ )*%' "#" $!' !*! *& !$ # & & & & & & & & & & & 3& !""(#"! $"#($ (!$! !(*$ "%) )!( !%( "& )% !) & & & & & & & & & & 4& )*#'($! $&$"" %$#) #'& %&& )!! !"# %) !& & % & & & & & & & & & 5& )(#&*$* %&$$$ !'() $%) !$$ )(* ## !! ) ) & & & & & & & & & & .' )!$!$)' %$&!! $#&' !"&& *"% !*# $# !( ! & & & & & & & & & & & /' !**$$$( %"$($ *'*( )'!$ #$* (*& )(" *' )( !( ) & & & & & & & & & 2' !*!!"(" %'##! *$#& !#&$ "$% %"$ !%% ($ !$ $ & & & & & & & & & & 3' !##&"$% (&&!( %*(# !%$( $!! )&$ !&( )( # $ & & & & & & & & & & & 4' !$&)#*) %*''% %&%# "*$ )*$ )%$ '# %) % $ & & & & & & & & & & & 5' )&'"!!! )$*'! !*#$ (&' !)' )&* !&! !& $ & & & & & & & & & & & /6789:;06<=;> ?=>9@6>78A9BC=

PAGE 123

! 111 !"" #$%& #'%( #'%& #)%( #)%& #*%( +$ !"#$%"& '%((& !)'($ ''!! *)*$ &%)! !%$& ,$ &**'*!% !%"%%" &&#"# !!!%# )"'" *)*" !"#$ ,$-. !("*$$' #%""( $$*! *'%% !*!$ '"' *#* /$ &*%*$&# ')##% !(#"$ '%)* &$*) !()* ")! 0$ &&!%%$* $#"&* !#!$& #$(# &'() !#)' '%" 1$ &)%#!*' !%&*#( !!))$ *"'$ !"%) !%!# )*( 2$ &#*%%'& "$$$( ))"' &!&$ !%&$ )%! #&" +' !)((*(' #(%"& !%(#( *)'& !#"* ))% !$' ,' !"#)$)! #$"$' !%$&' (!)( !)"" $*& ($( ,'-. !)(*()! &%*(% #&'! $") *&" *$ /' !''(('# ('((% !!#(# #!"$ !((% ')* &## 0' !"*$(!" )#)#' )"%& &)(! !!") #(# &#% 1' &'#(&*( (('"# (&%' !)&( '*( #*( &&# 2' &(!#!$% **(*# &$'$ !%*' (%( *(% !%# +) &!$#$)# #*#*( "#&# &)!( $!( &#& '# ,) !'!#)(! #$%$' !!((& #("" !)'* "!' *(' /) !))!*#% #$($* $'!& *!*& !*&' ('# !$$ 0) !$&))&) #("'* ("($ &&!! "(' *#) !#! 1) !(##&$) #!#*# ###! !#%* )*" *'* !*" 2) &!&(*#" &"&*' &(#) ")! #(& *&* !!' ,345678-39:8; <893"

PAGE 124

! 112 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% .# !"#$%& '#!$& (#)!& (#''& (#(!& (#(*& (#(+& (#('& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& /# !*#+%& +#""& (#)!& (#$%& (#$)& (#(%& (#(+& (#($& (#($& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& /#01 !,#)'& $#!*& (#+!& (#$*& (#(+& (#(+& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 2# !"#"%& '#"*& (#+,& (#$%& (#("& (#(+& (#('& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 3# !*#,$& +#"*& (#)'& (#$(& (#("& (#(+& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 4# !"#(,& +#)%& (#+(& (#(%& (#(+& (#($& (#($& (#((& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 5# !"#+(& +#)+& (#$!& (#(*& (#('& (#($& (#((& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& .& !,#'%& '#(!& (#)'& (#$+& (#(*& (#(+& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& /& !,#+(& '#$$& (#+$& (#$!& (#()& (#('& (#('& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& /&01 !%#,,& (#!,& (#'(& (#()& (#('& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 2& !"#,"& '#"(& (#)$& (#$*& (#()& (#(+& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 3& !"#)!& +#$)& (#'+& (#(%& (#()& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 4& !,#!,& $#%)& (#$+& (#(+& (#($& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 5& !%#",& $#''& (#(%& (#('& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& .( !%#('& $#"(& (#'"& (#(%& (#(+& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& /( !,#$)& '#$!& (#)$& (#$,& (#(*& (#(+& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 2( !,#($& '#)(& (#)(& (#$$& (#(*& (#('& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 3( !,#"'& '#(%& (#$!& (#(,& (#(+& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 4( !,#+'& '#)(& (#'(& (#(*& (#('& (#('& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 5( !%#",& $#'$& (#(%& (#('& (#($& (#($& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& (#((& 67 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% 89! 67 ( : #;( 67 <77 = =>?<@A"B"BC .# +#'* (#'+ (#(% (#(" (#() (#(+ (#(+ (#(' (#($ (#(( (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#** $#+' $($, !,, /# +#'' (#'! (#(% (#(* (#(" (#(* (#(+ (#(' (#(' (#(' (#(' (#($ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*, $#+) !%' !)' /#01 +#'! (#$" (#(" (#() (#($ (#(' (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $("$ $('$ 2# +#'" (#'$ (#(" (#(* (#(+ (#(' (#(' (#($ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*) $#+$ $()( $((( 3# +#'+ (#'! (#(, (#(+ (#(+ (#(' (#($ (#($ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#** $#+' $(+$ !!$ 4# +#') (#'% (#(* (#(' (#($ (#($ (#($ (#($ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*) $#+$ $(), $((, 5# +#'* (#', (#(+ (#($ (#($ (#(( (#(( (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $("( $('( .& +#'% (#$, (#(" (#() (#(' (#(' (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $("$ $('$ /& +#'% (#$, (#(* (#(* (#(' (#($ (#(' (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*) $#+( $(*, $($, /&01 +#++ (#(% (#(+ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*$ $#'! $$() $(") 2& +#', (#'$ (#(" (#() (#(' (#(' (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*) $#+$ $(*+ $($+ 3& +#'" (#'* (#() (#(' (#(' (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $("( $('( 4& +#+$ (#$* (#(' (#($ (#(( (#(( (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*' $#'! $(!' $(*' 5& +#++ (#$( (#($ (#($ (#(( (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*$ $#'! $$(* $("* .( +#+$ (#$+ (#() (#(' (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*' $#'! $(%" $()" /( +#'% (#$% (#(" (#(* (#(' (#(' (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*) $#+$ $(*) $($) 2( +#', (#$! (#(" (#(+ (#(' (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $("( $('( 3( +#'! (#$, (#(+ (#(' (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*' $#'! $(%$ $()$ 4( +#'% (#$! (#(+ (#($ (#($ (#($ (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*+ $#+( $(,% $(+% 5( +#++ (#$( (#($ (#($ (#(( (#($ (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( (#(( $#*$ $#'! $$(* $("* D"B>EABCGH" /AC<>IJ0AK"JB D"B>EABCGH" /AC<>IJ0AK"JB

PAGE 125

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

PAGE 126

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

PAGE 127

! 115 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% .# ! "#$%&' #($)*' &#$"+' %$((' ,$+*' &$#,' ($)"' ($)"' ($&)' ($(-' ($(&' ($(&' ($((' ($((' ($((' ($((' ($((' ($((' /# ! ,%$(*' #-$&%' &*$&&' "$+-' #$**' #$)(' #$#"' &$+)' ($%(' ($)*' ($#&' ($&,' ($(%' ($(*' ($()' ($(#' ($(&' ($(&' /#01 ! *)$,"' &)$,%' &#$((' *$,(' &$%-' ($")' ($)&' ($("' ($("' ($(,' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 2# ! "%$),' &-$))' -$-)' *$(+' ,$)%' &$#-' ($+%' ($#%' ($&)' ($(,' ($(+' ($()' ($((' ($((' ($((' ($((' ($((' ($((' 3# ! ))$,+' #*$(#' &"$,#' *$&)' ,$"&' &$%)' &$,&' ($%&' ($,(' ($#(' ($&#' ($()' ($(#' ($((' ($((' ($((' ($((' ($((' 4# ! ",$))' #($)#' -$++' )$+#' ,$&#' )$#"' #$**' ($-(' ($,&' ($#&' ($("' ($(%' ($((' ($(%' ($((' ($((' ($((' ($((' 5# ! "&$*+' #($&(' %$&,' ,$--' +$("' *$",' &$""' ($)+' ($&)' ($&)' ($(-' ($&)' ($((' ($((' ($((' ($((' ($((' ($((' .& ! "-$*&' ##$)&' &#$*&' )$&+' ($%)' ($##' ($(%' ($(,' ($(,' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' /& ! *+$,#' &)$*)' *$"#' +$""' #$-(' ($"%' ($#"' ($&#' ($(%' ($()' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' /&01 ! **$+,' #-$,&' ,$&)' ($)&' ($)&' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 2& ! *,$((' &%$+-' &#$,-' ,$%)' &$),' ($,*' ($&-' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 3& ! ""$#*' #+$*&' %$(+' "$("' #$*)' ($%+' ($)"' ($()' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 4& ! ")$++' &%$)*' &#$-%' &($-"' &$-+' ($*#' ($(*' ($((' ($&%' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 5& ! "&$,(' &)$-"' #,$+#' %$)-' &$(*' ($&(' ($&-' ($&-' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' .( ! *"$(&' #"$+)' *$)#' #$##' ($")' ($()' ($()' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' /( ! *,$")' &%$**' &($(,' "$,%' &$"(' ($"#' ($,&' ($()' ($(#' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 2( ! "+$*,' #)$()' &&$-+' )$#"' &$))' ($)%' ($&*' ($(,' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 3( ! *&$#)' #,$&&' -$#+' )$+(' &$(-' ($,*' ($#,' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 4( ! ")$",' &%$%-' &*$+"' *$--' #$#%' ($#&' ($,*' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 5( ! )+$"(' &)$-%' #,$-,' &&$+,' &$&*' ($"%' ($&#' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' ($((' 67 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% 89! 67 ( : #;( 67 <77 = =>?<@A"B"BC .# ! &)$#* %$++ %$() +$#)$+( #$(" ($-% &$#" ($)($,% ($(+ ($(% ($(( ($(( ($(( ($(( ($(( ($(( ,$*) ,$&( +,/# ! &($#% &#$"& &($,& "$#% ,$,# )$(( )$%* )$++ #$+" &$-) &$(* ($++ ($"($") ($,* ($#& ($&# ($&) )$(( ,$)( *( #( /#01 ! &+$,+ *$&* +$*% "$+) #$,* ($-( ($%% ($&" ($&($&& ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)* #$-) -# "# 2# ! &"$+% %$,, *$,* "$", )$," #$&) &$*% ($+% ($)($&# ($,* ($#* ($(( ($(( ($(( ($(( ($(( ($(( ,$",$(" %, ), 3# ! &&$-% &&$&* -$%& "$")$,,$(* #$%, #$## &$() ($%" ($*# ($#" ($&" ($(( ($(( ($(( ($(( ($(( ,$+% ,$#& +& ,& 4# ! &)$), %$+" *$#" )$,( ,$-( +$(% "$+) #$)% &$(* ($%+ ($#* ($)+ ($(( ($** ($(( ($(( ($(( ($(( ,$%, ,$#* *% #% 5# ! &,$-" %$*# "$#( ,$*) %$%& &($%* ,$," &$#($)% ($"($)% ($%+ ($(( ($(( ($(( ($(( ($(( ($(( ,$%+ ,$#** #* .& ! &*$&( -$*& %$(+ ,$%( &$(* ($,* ($&% ($(+ ($(($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)( #$%-+ "+ /& ! &%$&% *$#% )$&% *$%% ,$*, ($-+ ($") ($,# ($#+ ($&* ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)* #$-) -# "# /&01 ! &%$(# &#$"+ #$(& ($,+ ($"& ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$## #$+) &&) +) 2& ! &+$(& %$(* +$-, ,$"( &$+($*( ($)& ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)( #$%-+ "+ 3& ! &)$-# &&$%) "$&+ )$*& ,$,( &$)) ($-% ($&( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)#$-* -( "( 4& ! &)$++$-# %$,& -$-% #$)* &$(# ($&, ($(( ($*, ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$"* ,$(, %) )) 5& ! &,$%" *$)& &"$&% +$+, &$,, ($&* ($)# ($", ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$"+ ,$() %) )) .( ! &+$"" &&$(, )$&& #$(# ($*+ ($(* ($(% ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$##$+&(% *% /( ! &+$&" %$(( *$)# )$-& &$%% ($%+ ($** ($&# ($(+ ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$)# #$-& -" "" 2( ! &"$"* &($,& +$** ,$%+ &$%( ($%( ($,) ($(($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$), #$-# -" "" 3( ! &*$", -$-& "$-, )$#&$,* ($*( ($)($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$,#$%-% "% 4( ! &)$+# %$&( &($+# *$,+ #$%" ($,* ($++ ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$", ,$(( %+ )+ 5( ! &#$%, *$)# &"$,& &($*&$)" ($-+ ($#" ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ($(( ,$*, ,$(%( )( D"B>EABCGH" /AC<>IJ0AK"JB D"B>EABCGH" /AC<>IJ0AK"JB

PAGE 128

! 116 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% .# ! ! "#$#%& '%$%#& (%$)%& *$)*& '$%(& +$)%& +$)%& +$#+& +$()& +$+#& +$+#& +$++& +$++& +$++& +$++& +$++& +$++& /# ! ! "*$((& '%$+(& )$#,& "$')& #$--& #$%#& '$-(& ($')& +$*"& +$##& +$'+& +$(#& +$(+& +$+%& +$+#& +$+(& +$+(& /#01 ! ! "+$##& ##$%%& (*$%%& ,$#(& ($,'& ($("& +$(,& +$(,& +$+-& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 2# ! ! "%$*%& '#$)(& ("$%(& -$#-& #$(+& ($-*& +$%-& +$#"& +$+*& +$(*& +$(+& +$++& +$++& +$++& +$++& +$++& +$++& 3# ! ! "%$**& '*$,"& (($+#& %$#(& #$#+& '$#%& ($",& +$,"& +$#%& +$''& +$+*& +$+"& +$++& +$++& +$++& +$++& +$++& 4# ! ! "#$-,& '+$))& (+$(#& %$*+& )$("& ,$*+& ($)"& +$%%& +$""& +$((& +$(*& +$++& +$(*& +$++& +$++& +$++& +$++& 5# ! ! "($,)& (%$-(& -$'%& ("$,-& (#$,(& #$'(& +$)*& +$')& +$')& +$()& +$')& +$++& +$++& +$++& +$++& +$++& +$++& .& ! ! ,,$,+& #($''& (+$#'& '$+)& +$,"& +$'+& +$+*& +$+*& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& /& ! ! ""$*)& ()$)%& '#$(+& -$-)& ($*-& +$**& +$#%& +$'"& +$('& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& /&01 ! ! --$((& )$",& ($''& ($''& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 2& ! ! ,+$**& ##$"-& (+$#)& #$-*& +$)*& +$,'& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 3& ! ! %($*'& (-$+"& (($#+& ,$)+& ($)"& ($+(& +$+-& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 4& ! ! "+$-'& '-$*(& '"$''& "$#,& ($#%& +$("& +$++& +$"(& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 5& ! ! #+$%)& "-$*(& (*$"#& '$(-& +$'+& +$"+& +$"+& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& .( ! ! *#$,,& (-$#%& %$#"& ($,#& +$((& +$((& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& /( ! ! ,($(*& '*$,+& ("$*%& "$('& ($"#& +$-"& +$('& +$+%& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 2( ! ! ,%$*"& '-$'%& (+$+'& #$#)& ($(#& +$#-& +$+-& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 3( ! ! ,)$%#& '#$)'& ('$("& '$-+& +$)#& +$,-& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 4( ! ! "($,"& #%$-#& (,$#%& ,$+'& +$"*& +$*-& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 5( ! ! '-$,"& ",$,-& ''$#,& '$'(& ($((& +$''& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& +$++& 67 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% 89! 67 ( : #;( 67 <77 = =>?<@A"B"BC .# ! ! (-$,) (*$+" (,$", )$)% "$#" '$+'$%" ($+" +$-( +$(" +$(* +$++ +$++ +$++ +$++ +$++ +$++ "$(* #$," ,# (# /# ! ! '+$'+ (%$%, -$,' ,$#% %$"% *$-, *$*( "$"" #$(# ($*( ($', +$), +$-* +$,+$#" +$() +$'' "$"' #$*% "" /#01 ! ! (*$') '($," (%$(+ %$%# '$,' '$"% +$"' +$,' +$#' +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$+#$"* ,% (% 2# ! ! '+$+, (,$#+ (#$#( (+$"* ,$(% "$+, ($-* ($(* +$') +$-* +$%# +$++ +$++ +$++ +$++ +$++ +$++ "$(#$,% ,' (' 3# ! ! '+$+, (*$%# (+$+, *$-) ,$") ,$+) #$)) ($-* ($,# ($(( +$", +$'% +$++ +$++ +$++ +$++ +$++ "$'' #$,) ,( (( 4# ! ! (-$-+ (#$"# )$'# -$#* (,$'+ ('$#' ,$#' '$'($-* +$,* ($+' +$++ ($"' +$++ +$++ +$++ +$++ "$"#$-( "# # 5# ! ! (*$-# (+$*% *$,# (-$'' ''$"* %$)# '$%* ($++ ($'# ($++ ($*) +$++ +$++ +$++ +$++ +$++ +$++ "$,+ #$-# "' .& ! ! '#$*) ()$))$"+ '$%( +$)+ +$"" +$() +$'# +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$-% #$'%% '% /& ! ! ()$'+ ('$*'($+, (($(( '$)% ($%% +$)+$-( +$,+ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$(" #$,' ," (" /&01 ! ! #*$*%$+, ($(( ($,' +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$,) #$+% -' "' 2& ! ! '($** '($"# )$"* "$-" ($%( ($(( +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$)' #$## %# '# 3& ! ! '%$"% (($,, (+$#+ *$##$'# '$() +$'# +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$)" #$#, %' '' 4& ! ! (*$,+ (-$#* ''$+* ,$"" '$'% +$') +$++ ($"+ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$+* #$"% ,* (* 5& ! ! (#$(% #($((,$-'$*' +$## +$-% ($+) +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$+# #$"' ,) () .( ! ! #($," (($*, ,$*($)( +$(+$'" +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$*' #$(% *" #" /( ! ! '($)" (*$%+ (#$", ,$(% '$#) ($-( +$## +$'( +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$)#$#%( '( 2( ! ! '"$## (-$+) )$(# "$'" ($-+$-( +$'( +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$-) #$#+ %, ', 3( ! ! ',$,% (,$#( (($+% #$,+ ($,, ($'% +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ #$-#$') %% '% 4( ! ! (*$-( '#$,* ("$++ %$'* +$*($%) +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$++ #$"+ %+ '+ 5( ! ! ('$'" ')$(* '+$#% '$** ($-" +$"+$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ +$++ "$+% #$", ,* (* D"B>EABCGH" /AC<>IJ0AK"JB D"B>EABCGH" /AC<>IJ0AK"JB

PAGE 129

! 117 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% .# ! ! "#$%&' &($("' )"$%#' "$*)' )$#%' )$#%' %$+,' %$,"' %$%+' %$%+' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' /# ! ! "($)-' )#$*#' -$))' #$,"' *$-#' +$,)' &$"+' )$"%' %$*,' %$,-' %$&+' %$)(' %$))' %$%+' %$%,' %$%,' /#01 ! ! +*$"&' &($*)' -$-(' &$+"' )$()' %$&+' %$&+' %$),' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 2# ! ! ""$()' &#$"+' )+$#"' +$-&' ,$+&' )$&-' %$*"' %$),' %$,&' %$)(' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 3# ! ! +)$#"' &%$#&' ))$-*' *$&%' "$",' &$#,' )$%&' %$*-' %$")' %$)"' %$%#' %$%%' %$%%' %$%%' %$%%' %$%%' 4# ! ! ,#$,-' )-$%+' ))$(,' )*$&#' )%$)*' ,$"+' )$)-' %$#(' %$&%' %$,%' %$%%' %$,%' %$%%' %$%%' %$%%' %$%%' 5# ! ! &-$#(' )"$)"' &"$(*' &,$),' +$"(' )$**' %$+%' %$+%' %$,,' %$+%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' .& ! ! #%$)+' &,$)-' "$#%' )$&)' %$"+' %$)+' %$)+' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' /& ! ! ,*$)*' ")$-+' )*$%(' ,$&&' )$,(' %$*"' %$",' %$&)' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' /&01 ! ! #($"(' )%$&*' )%$&*' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 2& ! ! *-$%&' &)$)%' #$-*' )$(#' )$%+' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 3& ! ! "#$)"' &($+&' )+$"&' +$%#' &$*"' %$&&' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 4& ! ! "-$+)' "%$(&' #$,*' &$,%' %$&,' %$%%' %$*(' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 5& ! ! #%$&(' &+$)"' ,$)"' %$&(' %$+#' %$+#' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' .( ! ! *($"&' &,$(#' +$#(' %$")' %$")' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' /( ! ! +*$,%' ,%$&,' -$"+' &$("' )$#)' %$&"' %$)&' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 2( ! ! *+$,,' &,$)#' #$-"' &$*)' %$-#' %$)#' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 3( ! ! +($&+' ,%$%*' *$("' &$,)' )$"+' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 4( ! ! *,$%%' &*$&#' -$+-' %$-%' )$,"' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 5( ! ! *,$#-' ,)$&#' ,$)%' )$++' %$,)' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' %$%%' 67 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% 89! 67 ( : #;( 67 <77 = =>?<@A"B"BC .# ! ! ,%$%( &#$&)#$+( #$*# ,$*# "$** )$-, )$", %$&+ %$,% %$%% %$%% %$%% %$%% %$%% %$%% "$+* ,$-"% % /# ! ! ,)$"# )*$)) )%$)" )&$&) )"$-" )"$+# -$,( +$() ,$&" &$,* )$-% )$*+ )$)% %$*" %$,# %$"& +$%% "$&+ ,) !( /#01 ! ! ,*$)) &*$())$)& "$&, "$)& %$#% %$-# %$+" %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$,( ,$#, "+ + 2# ! ! &-$#" &+$%) )($*# ($*( #$*% ,$+) &$)( %$+" )$*" )$)%$%% %$%% %$%% %$%% %$%% %$%% "$*" ,$(" ,!& 3# ! ! ,,$)) )-$-)"$-, )%$,& ($+# #$"( ,$+) &$-&$%( %$-" %$+% %$%% %$%% %$%% %$%% %$%% "$#% "$%% ,# !, 4# ! ! &,$(& )*$"+ )"$(& &#$%# &)$(" ($""$%* ,$,, )$%) )$-& %$%% &$+" %$%% %$%% %$%% %$%% +$%& "$&# ,% !)% 5# ! ! )-$"& )&$-( ,)$&% ,-$"))$-* "$+# )$#) &$)) )$#% ,$%# %$%% %$%% %$%% %$%% %$%% %$%% +$%) "$&* ,% !)% .& ! ! ""$(% &)$)& +$-# &$%& %$(%$"& %$+& %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&, ,$*% +% )% /& ! ! &,$)" ,-$), &%$)& +$,* ,$%) )$## )$"# %$() %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$++ ,$-* ") ) /&01 ! ! +%$-# ($,+ )&$-& %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$),$++ +& )& 2& ! ! ",$+, )($&, ($-, ,$&# &$&* %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&# ,$*, "( ( 3& ! ! ,%$)# &*$(% )($&# -$", +$#) %$*% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$+% ,$-& "& & 4& ! ! ,)$%" ,#$&( ($&% ,$-& %$+% %$%% &$,# %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$,,$#, "+ + 5& ! ! ""$(&&$() ,$(, %$")$&, )$+# %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&& ,$+( +) )) .( ! ! ""$", &)$-" #$&, %$*( %$-( %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&& ,$+( +) )) /( ! ! ,*$%, &#$++ )%$+* "$-( ,$#% %$*# %$"& %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$,,$#& "* 2( ! ! ")$-) &)$)) ($-% "$,+ )$-%$"%$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$,% ,$*+ "3( ! ! ,#$(& &#$,( -$*# ,$-+ ,$)& %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$,, ,$*"# # 4( ! ! "%$,& &,$(" )%$#& )$," &$(% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&( ,$*+ "5( ! ! "%$-& &-$"( ,$-# &$+%$*# %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% "$&" ,$*) +% )% D"B>EABCGH" /AC<>IJ0AK"JB D"B>EABCGH" /AC<>IJ0AK"JB

PAGE 130

! 118 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% .# ! ! ! "#$"%& '#$"#& ($)%& *$'+& *$'+& +$%+& %$#,& %$%-& %$%-& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& /# ! ! ! *,$)(& +"$-"& +,$,,& +*$"'& +%$,,& ,$(+& '$)#& +$',& %$)#& %$,-& %$*(& %$''& %$++& %$%"& %$%"& /#01 ! ! ! #)$-*& '%$,+& "$(*& ,$*)& %$"(& %$"(& %$'-& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 2# ! ! ! ,-$(*& '($")& +%$")& #$*-& '$*'& +$+#& %$'*& %$"(& %$*"& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 3# ! ! ! ,'$-,& ',$"(& +'$("& -$+(& "$#"& '$+'& +$,+& %$("& %$'(& %$+,& %$%%& %$%%& %$%%& %$%%& %$%%& 4# ! ! ! '($('& +-$%#& '"$-(& +#$''& "$"+& +$(-& +$'#& %$*+& %$,)& %$%%& %$,)& %$%%& %$%%& %$%%& %$%%& 5# ! ! ! +-$(#& *"$%"& *'$,(& )$)+& '$*,& %$)%& %$)%& %$,)& %$)%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& .& ! ! ! ))$##& +"$),& ,$%#& +$"'& %$"+& %$"+& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& /& ! ! ! #"$""& '"$'+& "$%,& '$+(& +$%+& %$#)& %$*,& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& /&01 ! ! ! "%$%%& "%$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 2& ! ! ! #"$-(& ',$"-& #$+"& *$'(& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 3& ! ! ! ""$(*& '-$+)& -$"(& "$%%& %$,'& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 4& ! ! ! )-$,#& +,$'-& ,$,#& %$,"& %$%%& +$*,& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 5& ! ! ! (,$#'& +%$"(& %$-#& +$-'& +$-'& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& .( ! ! ! )($*(& +($-'& +$*"& +$*"& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& /( ! ! ! #-$+-& +-$**& #$)'& *$-'& %$"#& %$'(& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 2( ! ! ! ##$(*& ''$#+& )$",& '$"+& %$"%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 3( ! ! ! )*$)#& +)$%'& "$#)& *$""& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 4( ! ! ! )+$%+& '*$+-& '$+)& *$#'& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 5( ! ! ! (#$*'& ($""& ,$')& %$("& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& %$%%& 67 #$% &$' &$% ($' ($% )$' )$% %$' %$% *$' *$% +$' +$% ,$' ,$% -$' -$% #'$' #'$% ##$' ##$% 89! 67 ( : #;( 67 <77 = =>?<@A"B"BC .# ! ! ! "+$,**$'% +,$,) #$-' ($(% *$,# '$)% %$,) %$"# %$%% %$%% %$%% %$%% %$%% %$%% ,$-# ,$'' *+ !/# ! ! ! *+$#+-$-, ',$%' '-$'% '($#) +#$"+ ++$#, #$*) ,$#" *$"" *$'" '$+# +$'" %$)' %$(' "$#,$(, '+ !+/#01 ! ! ! #+$-% '"$"+ -$)% -$," +$#% '$%% +$'* %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$(+ ,$%*, !# 2# ! ! ! ,"$,% *"$)+ +)$"( +*$(% #$*( *$-( %$-( '$-) '$+, %$%% %$%% %$%% %$%% %$%% %$%% "$%" ,$'*% !+% 3# ! ! ! *-$+* *%$)' '+$*( +-$(* +"$"' )$') "$-# ,$*, +$)* +$%* %$%% %$%% %$%% %$%% %$%% "$'( ,$,'# !+, 4# ! ! ! '#$'# '*$(' ,*$'* *"$%, +"$+, #$,( "$*+ +$#+ '$-% %$%% ,$%" %$%% %$%% %$%% %$%% "$,) ,$#" '* !+) 5# ! ! ! +($+% ,*$(+ ",$%* +#$#" #$,' '$,% '$-# '$*,$*% %$%% %$%% %$%% %$%% %$%% %$%% "$** ,$"* '" !+" .& ! ! ! )%$)) +-$#) #$)# *$'+$*+$), %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)% *$-*) !* /& ! ! ! "-$)* *+$"+ ($*,$)' '$)) '$*+ +$,' %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$(% ,$%( *, !# /&01 ! ! ! ,"$"# #'$"% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)# ,$%" *" !" 2& ! ! ! #%$+* *%$), +%$'* )$%( %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)# ,$%" *" !" 3& ! ! ! "%$(( *#$,# +"$-, +%$(% +$+, %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$() ,$+, ** !) 4& ! ! ! )'$,+ +)$(# )$,* %$-# %$%% ,$"%$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$#*$-*) !* 5& ! ! ! ))$++ +*$'' +$#% ,$+" "$'( %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$## *$-# *( !' .( ! ! ! )+$,' '*$#" '$'" '$-' %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$#" *$-" *( !' /( ! ! ! #*$%" ',$+# ++$+( ($,) +$", %$-# %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)( ,$%# *" !" 2( ! ! ! #%$-% '($') +'$", "$,* +$*( %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)) ,$%" *" !" 3( ! ! ! #)$'+ '+$'( -$,, )$## %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)* ,$%' *# !, 4( ! ! ! #,$)+ '($-*$#' )$(* %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$)' ,$%+ *# !, 5( ! ! ! )($## +%$#( )$++ +$(" %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% %$%% ,$#' *$-' *!+ /AC<>DE0AF"EB G"B>HABCJK" /AC<>DE0AF"EB G"B>HABCJK"

PAGE 131

! 119 APPENDIX G 95 Span Girder Adjusted Results

PAGE 132

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

PAGE 133

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